Global 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...

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...

Springer Representations on the Khovanov Springer Varieties

Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S). We show that if Xn is embedded antipodally in (S) then the natural Sn-action on (S) induces an Sn-rep...