{"title":"Construction of one-fixed-point actions on spheres of nonsolvable groups II","authors":"M. Morimoto","doi":"10.2969/jmsj/89868986","DOIUrl":"https://doi.org/10.2969/jmsj/89868986","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"139 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139266753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Olgur Celikbas, Uyen Le, Hiroki Matsui, A. Sadeghi
{"title":"Remarks on a conjecture of Huneke and Wiegand and the vanishing of (co)homology","authors":"Olgur Celikbas, Uyen Le, Hiroki Matsui, A. Sadeghi","doi":"10.2969/jmsj/90749074","DOIUrl":"https://doi.org/10.2969/jmsj/90749074","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"427 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139270732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We shall propose a new proof scheme for Planar Cover Conjecture, focusing on the rotation systems of planar coverings of connected graphs. We shall introduce the notion of “rotation compatible coverings” and show that a rotation compatible covering of $G$ embedded on the sphere can be covered by a regular covering of $G$ embedded on an orientable closed surface on which its covering transformation group acts. The surface may not be homeomorphic to the sphere in general, but its quotient becomes either the sphere or the projective plane which contains $G$. As an application of our theory, we shall prove that if a 3-connected graph $G$ has a 3-connected finite planar covering such that the pre-images of each vertex has sufficiently large distance, then $G$ can be embedded on the projective plane.
{"title":"Another approach to Planar Cover Conjecture focusing on rotation systems","authors":"Seiya NEGAMI","doi":"10.2969/jmsj/90769076","DOIUrl":"https://doi.org/10.2969/jmsj/90769076","url":null,"abstract":"We shall propose a new proof scheme for Planar Cover Conjecture, focusing on the rotation systems of planar coverings of connected graphs. We shall introduce the notion of “rotation compatible coverings” and show that a rotation compatible covering of $G$ embedded on the sphere can be covered by a regular covering of $G$ embedded on an orientable closed surface on which its covering transformation group acts. The surface may not be homeomorphic to the sphere in general, but its quotient becomes either the sphere or the projective plane which contains $G$. As an application of our theory, we shall prove that if a 3-connected graph $G$ has a 3-connected finite planar covering such that the pre-images of each vertex has sufficiently large distance, then $G$ can be embedded on the projective plane.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"28 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134991937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order 8 and the cyclic group of order 2.
{"title":"Generalized Dedekind's theorem and its application to integer group determinants","authors":"Naoya YAMAGUCHI, Yuka YAMAGUCHI","doi":"10.2969/jmsj/90539053","DOIUrl":"https://doi.org/10.2969/jmsj/90539053","url":null,"abstract":"In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order 8 and the cyclic group of order 2.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"74 1-2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135272432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Time-dependent free surface problem for the incompressible Navier–Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We obtain global well-posedness of the problem for a small initial data in scale invariant critical Besov spaces. Our proof is based on maximal $L^{1}$-regularity of the corresponding Stokes problem in the half-space and special structures of the quasi-linear term appearing from the Lagrangian transform of the coordinate.
{"title":"Maximal $L^{1}$-regularity and free boundary problems for the incompressible Navier–Stokes equations in critical spaces","authors":"Takayoshi OGAWA, Senjo SHIMIZU","doi":"10.2969/jmsj/88288828","DOIUrl":"https://doi.org/10.2969/jmsj/88288828","url":null,"abstract":"Time-dependent free surface problem for the incompressible Navier–Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We obtain global well-posedness of the problem for a small initial data in scale invariant critical Besov spaces. Our proof is based on maximal $L^{1}$-regularity of the corresponding Stokes problem in the half-space and special structures of the quasi-linear term appearing from the Lagrangian transform of the coordinate.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove the convergence of (solid) ellipsoids to a Gaussian space in Gromov's concentration/weak topology as the dimension diverges to infinity. This gives the first discovered example of an irreducible nontrivial convergent sequence in the concentration topology, where ‘irreducible nontrivial’ roughly means to be not constructed from Lévy families nor box convergent sequences.
{"title":"High-dimensional ellipsoids converge to Gaussian spaces","authors":"Daisuke Kazukawa, Takashi Shioya","doi":"10.2969/jmsj/86648664","DOIUrl":"https://doi.org/10.2969/jmsj/86648664","url":null,"abstract":"We prove the convergence of (solid) ellipsoids to a Gaussian space in Gromov's concentration/weak topology as the dimension diverges to infinity. This gives the first discovered example of an irreducible nontrivial convergent sequence in the concentration topology, where ‘irreducible nontrivial’ roughly means to be not constructed from Lévy families nor box convergent sequences.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the parabolic BGG categories for graded Lie superalgebras of Cartan type over the field of complex numbers. The gradation of such a Lie superalgebra $mathfrak{g}$ naturally arises, with the zero component $mathfrak{g}_{0}$ being a reductive Lie algebra. We first show that there are only two proper parabolic subalgebras containing Levi subalgebra $mathfrak{g}_{0}$: the “maximal one” $mathsf{P}_{max}$ and the “minimal one” $mathsf{P}_{min}$. Furthermore, the parabolic BGG category arising from $mathsf{P}_{max}$ essentially turns out to be a subcategory of the one arising from $mathsf{P}_{min}$. Such a priority of $mathsf{P}_{min}$ in the sense of representation theory reduces the question to the study of the “minimal parabolic” BGG category $mathcal{O}^{min}$ associated with $mathsf{P}_{min}$. We prove the existence of projective covers of simple objects in these categories, which enables us to establish a satisfactory block theory. Most notably, our main results are as follows. (1) We classify and obtain a precise description of the blocks of $mathcal{O}^{min}$. (2) We investigate indecomposable tilting and indecomposable projective modules in $mathcal{O}^{min}$, and compute their character formulas.
{"title":"Parabolic BGG categories and their block decomposition for Lie superalgebras of Cartan type","authors":"Fei-Fei DUAN, Bin SHU, Yu-Feng YAO","doi":"10.2969/jmsj/90439043","DOIUrl":"https://doi.org/10.2969/jmsj/90439043","url":null,"abstract":"In this paper, we study the parabolic BGG categories for graded Lie superalgebras of Cartan type over the field of complex numbers. The gradation of such a Lie superalgebra $mathfrak{g}$ naturally arises, with the zero component $mathfrak{g}_{0}$ being a reductive Lie algebra. We first show that there are only two proper parabolic subalgebras containing Levi subalgebra $mathfrak{g}_{0}$: the “maximal one” $mathsf{P}_{max}$ and the “minimal one” $mathsf{P}_{min}$. Furthermore, the parabolic BGG category arising from $mathsf{P}_{max}$ essentially turns out to be a subcategory of the one arising from $mathsf{P}_{min}$. Such a priority of $mathsf{P}_{min}$ in the sense of representation theory reduces the question to the study of the “minimal parabolic” BGG category $mathcal{O}^{min}$ associated with $mathsf{P}_{min}$. We prove the existence of projective covers of simple objects in these categories, which enables us to establish a satisfactory block theory. Most notably, our main results are as follows. (1) We classify and obtain a precise description of the blocks of $mathcal{O}^{min}$. (2) We investigate indecomposable tilting and indecomposable projective modules in $mathcal{O}^{min}$, and compute their character formulas.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136210218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a continuum percolation built over stationary ergodic point processes. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies volume regularity and isoperimetric condition, we prove a quenched invariance principle for reflecting diffusions on the cluster.
{"title":"Quenched invariance principle for a reflecting diffusion in a continuum percolation cluster","authors":"Yutaka TAKEUCHI","doi":"10.2969/jmsj/89198919","DOIUrl":"https://doi.org/10.2969/jmsj/89198919","url":null,"abstract":"We consider a continuum percolation built over stationary ergodic point processes. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies volume regularity and isoperimetric condition, we prove a quenched invariance principle for reflecting diffusions on the cluster.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135695911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An element of a Weyl group of classical type is skew if it is the left factor in a reduced factorization of a Grassmannian element. The skew Grothendieck polynomials are those which are indexed by skew elements of the Weyl group. We define set-valued tableaux which are fillings of the associated skew Young diagrams and use them to prove tableau formulas for the skew double Grothendieck polynomials in all four classical Lie types. We deduce tableau formulas for the Grassmannian Grothendieck polynomials and the $K$-theoretic analogues of the (double mixed) skew Stanley functions in the respective Lie types.
{"title":"Tableau formulas for skew Grothendieck polynomials","authors":"Harry TAMVAKIS","doi":"10.2969/jmsj/89928992","DOIUrl":"https://doi.org/10.2969/jmsj/89928992","url":null,"abstract":"An element of a Weyl group of classical type is skew if it is the left factor in a reduced factorization of a Grassmannian element. The skew Grothendieck polynomials are those which are indexed by skew elements of the Weyl group. We define set-valued tableaux which are fillings of the associated skew Young diagrams and use them to prove tableau formulas for the skew double Grothendieck polynomials in all four classical Lie types. We deduce tableau formulas for the Grassmannian Grothendieck polynomials and the $K$-theoretic analogues of the (double mixed) skew Stanley functions in the respective Lie types.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to singularity theory but also to multiobjective optimization.
{"title":"A refined transversality theorem on linear perturbations and its applications","authors":"Shunsuke ICHIKI","doi":"10.2969/jmsj/90559055","DOIUrl":"https://doi.org/10.2969/jmsj/90559055","url":null,"abstract":"In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to singularity theory but also to multiobjective optimization.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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