Euler Characteristic of Springer fibers

TL;DR

This paper provides formulas for calculating Springer representations and Euler characteristics of Springer fibers for classical and exceptional types, advancing understanding of their algebraic and geometric properties.

Contribution

It introduces recursive formulas for Euler characteristics of Springer fibers and explicit tables for exceptional types, enhancing computational tools in representation theory.

Findings

Recursive formulas for Euler characteristics of Springer fibers.

Explicit tables for exceptional types.

Formulas for Springer representation restrictions.

Abstract

For Weyl groups of classical types, we present formulas to calculate the restriction of Springer representations to a maximal parabolic subgroup of the same type. As a result, we give recursive formulas for Euler characteristics of Springer fibers for classical types. We also give tables of those for exceptional types.