BFN 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...

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...

BfN-Skripten 362

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...