In [2] and [3], Arthur has formulated a number of conjectures about automorphic forms. These conjectures would have profound consequences for the unitary representation theory of the group G(R) of… (More)

The aim of this paper is two-fold. First, we compare two notions of a "space" of algebra structures over an operad A: 1. the classification space, which is the nerve of the category of weak… (More)

Let G be the split real form of a connected reductive algebraic group G. Let θ be a Cartan involution of G and K = G the corresponding maximal compact subgroup. Let B be a Borel subgroup of G with… (More)

The Langlands classiication theorem describes all admissible representations of a reductive group G in terms of the tempered representations of Levi subgroups of G. I will describe work with Susana… (More)

We study the restriction of minuscule representations to the principal SL2, and use this theory to identify an interesting test case for the Langlands philosophy of liftings. In this paper, we review… (More)

In [5], Aspnes, Herlihy, and Shavit generalized the notion of a sorting network by introducing a class of so called "counting" networks and establishing an O(lg2 n) upper bound on the depth… (More)

(Py,w;i ∈ N, u is an indeterminate) were defined and computed in terms of an algorithm for any y ≤ w in W . These polynomials are of interest for the representation theory of complex reductive… (More)

In this note we construct a “Kazhdan-Lusztig type” basis in equivariant K-theory of the nilpotent cone of a simple algebraic group G. This basis conjecturally is very close to the basis of this… (More)

Each subset is identified conjecturally (Conjecture 0.6) with a collection of unitary representations of a certain subgroup G(λu) of G. (We will give strong evidence and partial results for this… (More)