• Multiplicity formulas for finite dimensional and generalized principal series representations

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/106/04/0379-0401

• # Keywords

Reductive Lie algebra and subgroup; maximal compact group; weight; partition function; multiplicity; generalized principal series

• # Abstract

The article presents two results. (1) Let a be a reductive Lie algebra over ℂ and let b be a reductive subalgebra of a. The first result gives the formula for multiplicity with which a finite dimensional irreducible representation of b appears in a given finite dimensional irreducible representation of a in a general situation. This generalizes a known theorem due to Kostant in a special case. (2) LetG be a connected real semisimple Lie group andK a maximal compact subgroup ofG. The second result is a formula for multiplicity with which an irreducible representation ofK occurs in a generalized representation ofG arising not necessarily from fundamental Cartan subgroup ofG. This generalizes a result due to Enright and Wallach in a fundamental case.

• # Author Affiliations

1. Department of Mathematics, University of Bombay, Bombay - 400 098, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019