Injectivity of a certain cycle map for finite dimensional W-algebras

TL;DR

This paper proves the injectivity of a specific cycle map for finite-dimensional modules of W-algebras with regular integral central character, linking it to the topology of Springer fibers, advancing the understanding of W-algebra modules.

Contribution

It establishes the injectivity of a cycle map for finite-dimensional W-algebra modules, connecting algebraic and geometric perspectives in representation theory.

Findings

Cycle map injects into top Borel-Moore homology of Springer fibers

First step in classifying finite-dimensional W-algebra modules

Links algebraic modules to geometric topology

Abstract

We study a certain cycle map defined on finite dimensional modules for the W-algebra with regular integral central character. Via comparison with the theory in postive characteristic, we show that this map injects into the top Borel-Moore homology group of a Springer fibre. This is the first result in a larger program to completely desribe the finite dimensional modules for the W algebras.