Sam Evens

The Langlands classification for graded Hecke algebras

We establish the Langlands classification for graded Hecke algebras. The proof is analogous to the proof of the classification of highest weight modules for semisimple Lie algebras.

Characteristic cycles for the loop Grassmannian and nilpotent orbits

α (X), which is a linear combination of closures of conormal bundles to submanifolds of X. Intuitively, the microlocal multiplicities cα() me asurethesingularity of at α. In settings related to representation theory, a group G acts on X, is G-equivariant, and the microlocal multiplicities play a significant but only partially understood role in representation theory (see (Ro), (SV), (ABV), and (KaSa), e.g.). In this paper, we compute microlocal multiplicities for certain cases of interest in representation theory. Let G be a connected reductive group with loop group LG, and let P bethesubgroup of LG consisting of loops with positive Fourier coefficients. Then P -orbits λ on theloop Grassmannian LG/P = correspond to the irreducible representations L(λ) of thedual re ductivegroup ˇ G. For dominant weights µ and λ of a torus of ˇ

Thompson's conjecture for real semi-simple Lie groups

Aproof of Thompson’s conjecture for real semisimple Lie groups has been given by Kapovich, Millson, and Leeb. In this paper, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic geometry.

The relative Hochschild-Serre spectral sequence and the Belkale-Kumar product

We consider the Belkale-Kumar cup product

THE GELFAND-ZEITLIN INTEGRABLE SYSTEM AND K-ORBITS ON THE FLAG VARIETY

\odot_t

Representations of Quantum Tori and G-bundles on Elliptic Curves

on

Transverse measures, the modular class and a cohomology pairing for Lie algebroids

H^*(G/P)

On the variety of Lagrangian subalgebras, II

for a generalized flag variety

The Schubert calculus, braid relations, and generalized cohomology

G/P

Poisson Harmonic Forms, Kostant Harmonic Forms, and the S1-Equivariant Cohomology ofK/T☆

with parameter