2010/08/25 by Emiko Dupont, Dupont, Emiko
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.DG #math.RT
paper · pdf · doi:10.48550/arxiv.1008.4374
Masters thesis from 2003
arxiv created 2010/08/25 · arxiv updated 2010/08/27
Let G be a compact connected semisimple Lie group and let H⊂ G be a closed connected subgroup such that rank(G)=rank(H) and G/H is a symmetric space. Given an irreducible representation of H, we define a Dirac operator D and determine the representations of G in the kernel of D. Moreover, we show that any irreducible representation of G can be constructed in this way. Our approach is similar to that of Parthasarathy.