Estimates for kernels of intertwining operators on SL(n, R)

INTERTWINING DIFFERENTIAL OPERATORS FOR Mp ( « , R ) AND

For each of the two series of groups, three series of representations U„, D„, and H„ (n e Z) are considered. For each series of representations there is a differential operator with the property, that raised to the nth power (n > 0), it intertwines the representations indexed by — n and n. The operators are generalizations of the d'Alembertian, the Diracoperator and a combination of the two. Un...

(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 for the generalized principal series on a symmetric R-space

Three questions about the intertwining operators for the generalized principal series on a symmetric R-space are solved : description of the functional kernel, both in the noncompact and in the compact picture, domain of convergence, meromorphic continuation. A large use is made of the theory of positive Jordan triple systems. The meromorphic continuation of the intertwining integral is achieve...

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.