Mathematische Zeitschrift最新文献

We establish abstract Adams isomorphisms in an arbitrary equivariantly presentable equivariantly semiadditive global category. This encompasses the well-known Adams isomorphism in equivariant stable homotopy theory, and applies more generally in the settings of G-Mackey functors, G-global homotopy theory, and equivariant Kasparov categories.

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel–Lizorkin-type spaces (dot{B}^{s,tau }_{p,q}(W)) and (dot{F}^{s,tau }_{p,q}(W)). In this article, the authors establish the molecular and the wavelet characterizations of these spaces. Furthermore, as applications, the authors obtain the optimal boundedness of trace operators, pseudo-differential operators, and Calderón–Zygmund operators on these spaces. Due to the sharp boundedness of almost diagonal operators on their related sequence spaces obtained in the second article of this series, all results presented in this article improve their counterparts on matrix-weighted Besov and Triebel–Lizorkin spaces (dot{B}^{s}_{p,q}(W)) and (dot{F}^{s}_{p,q}(W)). In particular, even when reverting to the boundedness of Calderón–Zygmund operators on unweighted Triebel–Lizorkin spaces (dot{F}^{s}_{p,q}), these results are still better.

In a previous part of this work, we gave a new tableau formula for the modified Macdonald polynomials (widetilde{H}_{lambda }(X;q,t)), using a weight on tableaux involving the queue inversion (quinv) statistic. In this paper we explicitly describe a connection between these combinatorial objects and a class of multispecies totally asymmetric zero range processes (mTAZRP) on a ring, with site-dependent jump-rates. We construct a Markov chain on the space of tableaux of a given shape, which projects to the mTAZRP, and whose stationary distribution can be expressed in terms of quinv-weighted tableaux. We deduce that the mTAZRP has a partition function given by the modified Macdonald polynomial (widetilde{H}_{lambda }(X;1,t)). The novelty here in comparison to previous works relating the stationary distribution of integrable systems to symmetric functions is that the variables (x_1,ldots ,x_n) are explicitly present as hopping rates in the mTAZRP. We also obtain interesting symmetry properties of the mTAZRP probabilities under permutation of the jump-rates between the sites. Finally, we explore a number of interesting special cases of the mTAZRP, and give explicit formulas for particle densities and correlations of the process purely in terms of modified Macdonald polynomials.

In this paper, we define and study Clifford quadratic complete intersections. After showing some properties of Clifford quantum polynomial algebras, we show that there is a natural one-to-one correspondence between Clifford quadratic complete intersections and commutative quadratic complete intersections. We also provide a calculation method for the point varieties of Clifford quadratic complete intersections. As an application, we give a classification of Clifford quadratic complete intersections in three variables in terms of their characteristic varieties.

We give a two-variable Rankin–Selberg integral for generic cusp forms on (textrm{PGL}_4) and (textrm{PGU}_{2,2}) which represents a product of exterior square L-functions. As a residue of our integral, we obtain an integral representation on (textrm{PGU}_{2,2}) of the degree 5 L-function of ({textrm{GSp}}_4) twisted by the quadratic character of E/F of cuspidal automorphic representations which contribute to the theta correspondence for the pair ((textrm{P}{textrm{GSp}}_4,textrm{P}{textrm{GU}}_{2,2})).

We study the mapping properties of the Hardy–Littlewood fractional maximal operator between Lorentz spaces of the homogeneous tree and discuss the optimality of all the results.

In this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case the homotopy type of this simplicial complex coincides with that of the Tits building thanks to a well-known result of Quillen. On the other hand, in the non-defining characteristic case, we show that the simplicial complex of Brauer pairs is homotopy equivalent to a simplicial complex determined by generalised Harish-Chandra theory. This extends earlier results of the author on the Brown complex and makes use of the theory of connected subpairs and twisted block induction developed by Cabanes and Enguehard.

Let Y be a smooth quartic double solid regarded as a degree 4 hypersurface of the weighted projective space (mathbb {P}(1,1,1,1,2)). We study the multiplication of the Hochschild-Serre algebra of its Kuznetsov component (mathcal {K}u(Y)) via matrix factorization. As an application, we give a new disproof of Kuznetsov’s Fano threefold conjecture.

We use a Koszul-type resolution to prove a weak version of Bott’s vanishing theorem for smooth hypersurfaces in (mathbb {P}^n) and use this result to prove a vanishing theorem for Hodge ideals associated to an effective Cartier divisor on a hypersurface. This extends an earlier result of Mustaţă and Popa.

Let X be a non-singular compact complex surface such that the anticanonical line bundle admits a smooth Hermitian metric with semi-positive curvature. For a non-singular hypersurface Y which defines an anticanonical divisor, we investigate the (overline{partial }) cohomology group (H^1(M, mathcal {O}_M)) of the complement (M=Xsetminus Y).