论文标题
分级的Hecke代数和nilpotent圆锥上的均衡管
Graded Hecke algebras and equivariant constructible sheaves on the nilpotent cone
论文作者
论文摘要
分级的Hecke代数可以几何构建，具有可构造的滑轮和均衡的共同体。该输入由G型G（可能是断开连接的）G组（可能是断开连接的）和G的局部系统组成的G。锥$ g_n $。 从那里，我们提供了$ g_n $上的构造式滑轮的g x c*-equivariant有限派生类别的代数描述。也就是说，它与有限生成的差异分级模块的有界派生类别相等，该模块的分级为代数合适的直接总和。这可以被视为分级Hecke代数的分类。
Graded Hecke algebras can be constructed geometrically, with constructible sheaves and equivariant cohomology. The input consists of a complex reductive group G (possibly disconnected) and a cuspidal local system on a nilpotent orbit for a Levi subgroup of G. We prove that every such "geometric" graded Hecke algebra is naturally isomorphic to the endomorphism algebra of a certain G x C*-equivariant semisimple complex of sheaves on the nilpotent cone $g_N$. From there we provide an algebraic description of the G x C*-equivariant bounded derived category of constructible sheaves on $g_N$. Namely, it is equivalent with the bounded derived category of finitely generated differential graded modules of a suitable direct sum of graded Hecke algebras. This can be regarded as a categorification of graded Hecke algebras.
