Homology of generalized Steinberg varieties and Weyl group invariants

Homology of Generalized Steinberg Varieties and Weyl Group Invariants

Let G be a complex, connected, reductive algebraic group. In this paper we show analogues of the computations by Borho and MacPherson of the invariants and antiinvariants of the cohomology of the Springer fibres of the cone of nilpotent elements, N , of Lie(G) for the Steinberg variety Z of triples. Using a general specialization argument we show that for a parabolic subgroup WP ×WQ of W × W th...

Homology of the Steinberg Variety and Weyl Group Coinvariants

LetG be a complex, connected, reductive algebraic group with Weyl groupW and Steinberg variety Z. We show that the graded Borel-Moore homology of Z is isomorphic to the smash product of the coinvariant algebra of W and the group algebra of W . 2000 Mathematics Subject Classification: Primary 20G05; Secondary 20F55

Hall Invariants, Homology of Subgroups, and Characteristic Varieties

Given a finitely-generated group G, and a finite group Γ, Philip Hall defined δΓ(G) to be the number of factor groups of G that are isomorphic to Γ. We show how to compute the Hall invariants by cohomological and combinatorial methods, when G is finitely-presented, and Γ belongs to a certain class of metabelian groups. Key to this approach is the stratification of the character variety, Hom(G,K...

Homological realization of Nakajima varieties and Weyl group actions

Reflection Functors for Quiver Varieties and Weyl Group Actions

We define a Weyl group action on quiver varieties using reflection functors, which resemble ones introduced by Bernstein-Gelfand-Ponomarev [1]. As an application, we define Weyl group representations of homology groups of quiver varieties. They are analogues of Slodowy’s construction of Springer representations of the Weyl group.