Elliptic Springer theory

Introduction to Springer theory

(d) Hm−∗(M,M \X), where M is a smooth oriented manifold of dimension m and there exists an embedding X ↪→M as before. (d’) Hm−∗(X) if X itself is a smooth oriented manifold of dimension m. (e) H∗(D•(X), d). Assume there exists an embedding X ↪→M to a smooth manifold M of dimension m. Then we define D•(X) be a chain complex of distributions supported on X. (A distributions of degree k is a conti...

Characters of Springer Representations on Elliptic Conjugacy Classes

For a Weyl group W , we investigate simple closed formulas (valid on elliptic conjugacy classes) for the character of the representation of W in the homology of a Springer fiber. We also give a formula (valid again on elliptic conjugacy classes) of the W -character of an irreducible discrete series representation with real central character of a graded affine Hecke algebra with arbitrary parame...

Springer Theory via the Hitchin Fibration

In this paper, we translate the Springer theory of Weyl group representations into the language of symplectic topology. Given a semisimple complex group G, we describe a Lagrangian brane in the cotangent bundle of the adjoint quotient g/G that produces the perverse sheaves of Springer theory. The main technical tool is an analysis of the Fourier transform for constructible sheaves from the pers...

Game Theory and Information Economics Springer-verlag

Springer Theory for Complex Reflection Groups

Many complex reflection groups behave as though they were the Weyl groups of “nonexistent algebraic groups”: one can associate to them various representation-theoretic structures and carry out calculations that appear to describe the geometry and representation theory of an unknown object. This paper is a survey of a project to understand the geometry of the “unipotent variety” of a complex ref...