Quiver Hecke algebras for Borcherds-Cartan datum
英文摘要:
We introduce a family of quiver Hecke algebras which give a categorification of quantum Borcherds algebra associated to an arbitrary Borcherds-Cartan datum.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Bolun Tong, Wan Wu
We introduce a family of quiver Hecke algebras which give a categorification of quantum Borcherds algebra associated to an arbitrary Borcherds-Cartan datum.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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Quiver Hecke algebras for Borcherds-Cartan datum II
本文给出了箭图Hecke代数不可约模Grothendieck群的晶体结构,实现了量子Borcherds代数晶体$B(\infty)$与$B(\lambda)$的范畴化,并研究了不可约最高权模的循环范畴化。
On the cyclotomic Hecke algebras of complex reflection groups
继定义Rouquier的“家庭的字符”的外尔群和其推广的情况下,复杂的反射群,已经出现在工作的Broue-Kim和马勒Rouquier,我们表明,这些“家庭”依赖于一个数字数据的组,它的“本质超平面”。利用这一特征,我们提供了所有例外复反射群的分圆Hecke代数的Rouquier块的确定算法和结果。
A Langlands duality of elliptic Hecke algebras
本文通过椭圆Hecke代数与动力学参数建立联络,建立椭圆affine Hecke代数表示范畴与Langlands对偶根datum对应范畴之间的傅里叶-穆卡伊 functor。
Unitary equivalences for reductive p-adic groups
在类型论的框架下,我们建立了约化p-adic群的光滑表示范畴的Bernstein分支到相应的Hecke代数的酉性的转移,只要Hecke代数是具有几何参数的仿射Hecke代数,在Lusztig意义下(可能由根数据的自同构群扩展).众所周知,有一大类这样的例子(在论文中详细介绍)。因此,我们在内窥镜检查的精神下,建立了不同群体之间的整体性联系。
We introduce the notion of affinizations and R-matrices for arbitrary quiver Hekcke algebras. We show that they enjoy similar properties to those for symmetric quiver Hecke algebras. We next define the notion of a duality datum and construct a tensor functor between graded module categories of two quiver Hecke algebras. We give several examples of such functors .
Le lemme fondamental pour l'endoscopie tordue: le cas o{ù} le groupe endoscopique non ramifi{é} est un tore
本文证明了球面Hecke代数的单位元的扭曲内窥镜的基本引理,其基础群是环面的非分歧椭圆内窥镜数据。这意味着扭曲内窥镜的基本引理现在被证明,对于球面Hecke代数中的所有元素,在特征零和任何剩余特征。
Defect in cyclotomic Hecke algebras
本文证明了亏格在无限系列复反射群及分圆Yokonuma-Hecke代数中是块不变量,并揭示了其与Fayers权概念及钩长推广的对应关系。
Let H = H (R,q) be an affine Hecke algebra with complex, possibly unequal parameters q, which are not roots of unity. We compute the Hochschild and the cyclic homology of H. It turns out that these are independent of q and that they admit an easy description in terms of the extended quotient of a torus by a Weyl group, both of which are canonically associated to the root datum R. For q positive we also prove that the representations of the family of algebras H (R,q^ε) come in families which depend analytically on the complex number ε. Analogous results are obtained for graded Hecke algebras an…
On the center of the generic affine Hecke algebra
本文确定了一般仿射Hecke代数的中心为优势腔半群代数,并通过极大交换子代数将其与环面簇的量子上同调联系起来。
Let G be a reductive p-adic group and let H(G)^s be a Bernstein block of the Hecke algebra of G. We consider two important topological completions of H(G)^s: a direct summand S(G)^s of the Harish-Chandra--Schwartz algebra of G and a two-sided ideal C*_r (G)^s of the reduced C*-algebra of G. These are useful for the study of all tempered smooth G-representations. We suppose that H(G)^s is Morita equivalent to an affine Hecke algebra H(R,q) -- as is known in many cases. The latter algebra also has a Schwartz completion S(R,q) and a C*-completion C*_r (R,q), both defined in terms of the underlyin…
For symmetric groups we show that the p-canonical basis can be extended to a cell datum for the Iwahori-Hecke algebra H and that the two-sided p-cell preorder coincides with the Kazhdan-Lusztig two-sided cell preorder. Moreover, we show that left (or right) p-cells inside the same two-sided p-cell for Hecke algebras of finite crystallographic Coxeter systems are incomparable (Property A).
On the classification of irreducible representations of affine Hecke algebras with unequal parameters
设$R$是仿射Weyl群$W^e$的根数据,$H = H (R,q)$是仿射Hecke代数,其参数$q$为正,且可能不相等.那么$H$是群代数$\mathbb C [W^e]$的变形,所以比较$H$和$W^e$的表示理论是很自然的。我们定义了一个映射从不可约$H$ -表示$W^e$ -表示,我们表明,当扩展到Grothendieck群的有限维表示,这个映射成为同构,模扭转。映射可以被调整为从$H$的对偶空间到$W^e$的对偶空间的(非自然的)连续双射。我们用它来证明仿射Hecke代数版本的猜想的奥伯特,鲍姆和Plymen,它预测一个强大的和明确的几何相似性之间的对偶空间的$H$和$W^e$。一个重要的作用是发挥施瓦茨完成$S = S (R,q)$的$H$,代数的表示正是回火$H$ -表示。我们构造同构$ζ_ε: S (R,q^ε) \to S (R,q)$ $(ε>0)$和注入$ζ_0 : S (W^e) = S (R,q^0) \to S (R,q)$,连续依赖于$ε$。虽然$ζ_0$不是满射,但它在许多方面表现得像代数同构。$ζ_0$不仅扩展到有限维表示的Grothendieck群上的双射,它还在拓扑$K$ -理论和周期循环同调(前两个模挠)上诱导同构。这证明了Higson和Plymen的一个猜想,即仿射Hecke代数$H (R,q)$的$C^*$ -完备化的$K$ -理论不依…
Pinned Jordan Decomposition of Characters and Depth-Zero Hecke Algebras
本文研究了有限缩减群中相关对偶中心化子可能不连通时的固定约当分解构造,通过Pinning和Deligne-Lusztig公式建立了Lusztig系列与单因子的对应关系,同时探讨了具有阿贝尔组件群的可能不连通缩减群的约当分解扩展。
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