The stability of graded multiplicity in the setting of the Kostant-Rallis theorem

Abstract

From a combinatorial point of view, we approach the problem of finding a graded generalization of the Kostant-Rallis theorem concerning the K-harmonic polynomials on p. Specifically, for each classical symmetric pair we obtain a stable range where the multiplicity of an irreducible K-representation in the degree d harmonic polynomials can be expressed in terms of Littlewood-Richardson coefficients. © 2008 Birkhäuser Boston.