Graded multiplicities in the Kostant-Rallis setting

Mr. Andrew Frohmader
Graduate Student
University of Wisconsin-Milwaukee

This dissertation contains two main results. First, we provide combinatorial branching rules for GL(n, C) to O(n, C) and GL(2n, C) to Sp(2n, C) extending the Littlewood restriction rules. Second, we use these branching rules and the combinatorics of GL(n, C)-crystals to derive a formula for the graded multiplicity of a K-type in the regular functions on the K-nilpotent cone for GL(n, R), GL(n, C) and GL(n, H).

Advisor:
Jeb Willenbring

Committee Members:
Allen Bell, Chris Hruska, Istvan Lauko, and Kevin McLeod