The aim of this paper is to prove two general results on parabolic induction of classical p-adic groups (actually, one of them holds also in the archimedean case), and to obtain from them some consequences about irreducible unitarizable representations. One of these consequences is a reduction of the unitarizability problem for these groups. This reduction is similar to the reduction of the uni...

Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit several descriptions as superfields on different superspaces. In particular, this is the case for on-shell massless superfields. This allows a description of sh...

We examine the theory of induced representations for non-connected reductive p-adic groups for which G/G is abelian. We first examine the structure of those representations of the form IndGP 0(σ), where P 0 is a parabolic subgroup of G and σ is a discrete series representation of the Levi component of P . Here we develop a theory of R–groups, extending the theory in the connected case. We then ...

Introduction 1 1. Finite-dimensional case 4 2. The case of affine algebras 8 3. Comparison of cohomology classes 19 4. Wakimoto modules of critical level 25 5. Deforming to other levels 33 6. Semi-infinite parabolic induction 40 7. Wakimoto modules over ŝl2 46 8. Intertwining operators for an arbitrary g 51 9. Description of the center of Vκc(g) 57 10. Opers and Miura opers 66 11. Identificatio...

Let G be a reductive algebraic group defined over an algebraically closed field k. Let H be a closed connected subgroup of G containing a maximal torus T of G. In [13] it was shown (at least in characteristic zero) that the parabolic subgroups of G can be characterized among all such subgroups H by a certain finiteness property of the induction functor (-)Iz and its derived functors Lk,G(-). Th...

We associate a two-sided cell to any (parabolic) character sheaf. We study the interaction between the duality operator for character sheaves and the operation of “twisted induction”.

In 1986, George Lusztig stated some interesting properties of character sheaves with non-zero restriction to the unipotent variety and proved them for the group SO2n+1(Fq) under the assumption that the characteristic p of Fq is good. In February 1992, the author has given lectures on that proof of Lusztig in the Seminar “Faisceaux Caractères” at the École Normale Supérieure and it was no doubt ...

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 Salamanca-Riba that provides (conjecturally) a similar description of the unitary representations of G in terms of certain very special unitary representations of Levi subgroups. x1. Introduction Sup...