Homology of the Steinberg Variety and Weyl Group Coinvariants

Let $G$ be a complex, connected, reductive algebraic group with Weyl group $W$ 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

Keywords and Phrases: Borel-Moore Homology, Steinberg Variety, Coinvariant algebra, Weyl group

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