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The Adams isomorphism revisited 亚当斯同构问题再探讨
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-09-18 DOI: 10.1007/s00209-024-03582-w
Bastiaan Cnossen, Tobias Lenz, Sil Linskens

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.

我们在任意等变现存等变半增全局范畴中建立了抽象亚当斯同构。这包括等变稳定同构理论中著名的亚当斯同构,并更普遍地适用于 G-Mackey 函数、G-全局同构理论和等变卡斯帕罗夫范畴。
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引用次数: 0
Matrix-weighted Besov-type and Triebel–Lizorkin-type spaces III: characterizations of molecules and wavelets, trace theorems, and boundedness of pseudo-differential operators and Calderón–Zygmund operators 矩阵加权贝索夫型和特里贝尔-利佐尔金型空间 III:分子和小波的特性、迹定理以及伪微分算子和卡尔德龙-齐格蒙算子的有界性
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-09-15 DOI: 10.1007/s00209-024-03584-8
Fan Bu, Tuomas Hytönen, Dachun Yang, Wen Yuan

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.

这是作者连续发表的三篇关于矩阵加权贝索夫型和特里贝尔-利佐金型空间(dot{B}^{s,tau }_{p,q}(W))和(dot{F}^{s,tau }_{p,q}(W))的文章中的最后一篇。在本文中,作者建立了这些空间的分子特征和小波特征。此外,作为应用,作者还得到了这些空间上的迹算子、伪微分算子和卡尔德龙-齐格蒙算子的最优有界性。由于在本系列的第二篇文章中得到了几乎对角线算子在其相关序列空间上的尖锐有界性,本文提出的所有结果都改进了它们在矩阵加权贝索夫和特里贝尔-利佐金空间(dot{B}^{s}_{p,q}(W))和(dot{F}^{s}_{p,q}(W))上的对应结果。特别是,即使回到无权特里贝尔-利佐金空间 (dot{F}^{s}_{p,q})上的卡尔德龙-齐格蒙算子的有界性,这些结果仍然更好。
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引用次数: 0
Modified Macdonald polynomials and the multispecies zero range process: II 修正的麦克唐纳多项式和多物种零范围过程:二
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-09-13 DOI: 10.1007/s00209-024-03548-y
Arvind Ayyer, Olya Mandelshtam, James B. Martin

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.

在这项工作的前一部分,我们给出了修正麦克唐纳多项式(widetilde{H}_{lambda }(X;q,t))的新表符公式,使用了涉及队列反转(quinv)统计量的表符权重。在本文中,我们明确描述了这些组合对象与环上一类多物种完全非对称零范围过程(mTAZRP)之间的联系,该过程具有依赖于站点的跳跃率。我们在给定形状的表格空间上构建了一个马尔可夫链,它投影到 mTAZRP,其静态分布可以用 quinv 加权表格来表示。我们推导出,mTAZRP 有一个由修正麦克唐纳多项式给出的分割函数 (widetilde{H}_{lambda }(X;1,t)) 。与之前将可积分系统的静态分布与对称函数相关联的工作相比,这里的新颖之处在于变量 (x_1,ldots ,x_n)在 mTAZRP 中明确地作为跳跃率存在。我们还得到了 mTAZRP 概率在站点间跳跃率排列下的有趣对称性。最后,我们探讨了 mTAZRP 的一些有趣特例,并给出了纯粹以修正麦克唐纳多项式表示的粒子密度和过程相关性的明确公式。
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引用次数: 0
Clifford quadratic complete intersections 克利福德二次完全交叉
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-09-04 DOI: 10.1007/s00209-024-03575-9
Haigang Hu, Izuru Mori

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.

在本文中,我们定义并研究了克利福德二次完全交集。在展示了克利福德量子多项式代数的一些性质之后,我们证明了克利福德二次完全交集与交换二次完全交集之间存在天然的一一对应关系。我们还提供了克利福德二次完全交点品种的计算方法。作为应用,我们给出了三变量克利福德二次完全相交的特征品种分类。
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引用次数: 0
A two variable Rankin–Selberg integral for $${textrm{GU}}(2,2)$$ and the degree 5 L-function of $${textrm{GSp}}_4$$ $${textrm{GU}}(2,2)$$ 和 $${textrm{GSp}}_4$$ 的 5 级 L 函数的两变量兰金-塞尔伯格积分
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-09-03 DOI: 10.1007/s00209-024-03583-9
Antonio Cauchi, Armando Gutierrez Terradillos

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})).

我们给出了在(textrm{PGL}_4)和(textrm{PGU}_{2,2})上一般尖顶形式的双变量兰金-塞尔伯格积分,它表示外部平方 L 函数的乘积。作为积分的残差,我们在 (textrm{PGU}_{2、2})上的一个积分表示,它是({textrm{GSp}}_4)的阶 5 L 函数,它被尖顶自形表示的 E/F 的二次方特征扭曲了,这有助于一对 ((textrm{P}{textrm{GSp}}_4,textrm{P}{textrm{GU}}_{2,2})的θ 对应。)
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引用次数: 0
Hardy–Littlewood fractional maximal operators on homogeneous trees 同质树上的哈代-利特尔伍德分数最大算子
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-08-29 DOI: 10.1007/s00209-024-03574-w
Matteo Levi, Federico Santagati

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.

我们研究了哈代-利特尔伍德分数最大算子在同质树洛伦兹空间之间的映射特性,并讨论了所有结果的最优性。
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引用次数: 0
The simplicial complex of Brauer pairs of a finite reductive group 有限还原群的布劳尔对的简单复数
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-08-23 DOI: 10.1007/s00209-024-03579-5
Damiano Rossi

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.

在本文中,我们研究了有限还原群族的布劳尔对的包含排序的正集所诱导的简单复数。在定义特征情况下,由于奎伦(Quillen)的一个著名结果,这个简单复数的同调类型与蒂茨楼的同调类型重合。另一方面,在非定义特征情况下,我们证明布劳尔对的单纯复数与广义哈里什-钱德拉理论确定的单纯复数同调等价。这扩展了作者早先关于布朗复数的结果,并利用了卡巴内斯和恩格哈德发展的连通子对理论和扭块归纳法。
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引用次数: 0
Kuznetsov’s Fano threefold conjecture via Hochschild–Serre algebra 库兹涅佐夫通过 Hochschild-Serre 代数的法诺三折猜想
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-08-21 DOI: 10.1007/s00209-024-03586-6
Xun Lin, Shizhuo Zhang

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.

设 Y 是光滑的四元二次实体,视为加权投影空间 (mathbb {P}(1,1,1,1,2)) 的 4 度超曲面。我们通过矩阵因式分解来研究其库兹涅佐夫分量 (mathcal {K}u(Y)) 的霍赫希尔德-塞雷代数的乘法。作为应用,我们给出了库兹涅佐夫法诺三折猜想的新反证。
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引用次数: 0
Vanishing theorem for Hodge ideals on smooth hypersurfaces 光滑超曲面上霍奇理想的消失定理
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-08-21 DOI: 10.1007/s00209-024-03576-8
Anh Duc Vo

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.

我们利用科斯祖尔型解析证明了 Bott's vanishing theorem 的弱版本,即在(mathbb {P}^n) 中的光滑超曲面的消失定理,并利用这一结果证明了与超曲面上有效卡蒂埃除数相关的霍奇理想的消失定理。这扩展了穆斯塔法和波帕的一个早期结果。
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引用次数: 0
$$overline{partial }$$ cohomology of the complement of a semi-positive anticanonical divisor of a compact surface $$overline{partial }$$ 紧凑表面的半正反锥分裂子的补集同调
IF 0.8 3区 数学 Q1 MATHEMATICS Pub Date : 2024-08-20 DOI: 10.1007/s00209-024-03587-5
Takayuki Koike

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).

让 X 是一个非邢状紧凑复曲面,使得反锥线束具有半正曲率的光滑赫米特度量。对于定义了反偶函数除数的非星超曲面 Y,我们研究了补集(M=Xsetminus Y)的同调群(H^1(M, mathcal {O}_M))。
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Mathematische Zeitschrift
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