Action of intertwining operators on pseudospherical K-types

Action of Intertwining Operators on Pseudo-spherical K-types

In this paper, we give a concrete description of the two-fold cover of a simply connected, split real reductive group and its maximal compact subgroup as Chevalley groups. We study the representations of the maximal compact subgroups called pseudospherical representations which appear with multiplicity one in the principal series representation. We introduce a family of canonically defined inte...

(k, r)-ADMISSIBLE CONFIGURATIONS AND INTERTWINING OPERATORS

Certain combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level k standard modules for affine Lie algebra sl(r, C)̃ are parametrized by (k, r)-admissible configurations. In this note we use Capparelli-LepowskyMilas’ method to give a new proof of linear independence of these bases, the main ingredient in the proof being the use of Dong-Lepowsky’s intertwining operators for fundamental...

Intertwining Operators and Residues

Intertwining Operators between Line Bundles on Grassmannians

Let G = GL(n, F ) where F is a local field of arbitrary characteristic, and let π1, π2 be representations induced from characters of two maximal parabolic subgroups P1, P2. We explicitly determine the space HomG (π1, π2) of intertwining operators and prove that it has dimension ≤ 1 in all cases.

Traces of intertwining operators and

Traces of intertwining operators and Macdonald's polynomials Alexander A. Kirillov, Jr. May 1995 Let : V ! V U be an intertwining operator between representations of a simple Lie algebra (quantum group, a ne Lie algebra). We de ne its generalized character to be the following function on the Cartan subalgebra with values in U : (h) = TrV ( eh). This is a generalization of usual characters. Thes...