Boundaries of K-types in discrete series

• Main Author: Havlíčková, Markéta
• Other Authors: Michael J. Hopkins and David A. Vogan.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2008
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/43796

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. === Includes bibliographical references (p. 75-76). === Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we have a formula that gives the multiplicity of any given irreducible K-representation (or K-type) as an alternating sum. It is not immediately clear from this formula which K-types, indexed by their highest weights, have non-zero multiplicity. Evidence suggests that the collection is very close to a set of lattice points in a noncompact convex polyhedron. In this paper we shall describe a recursive algorithm for finding the boundary facets of this polyhedron. === by Markéta Havlíčková. === Ph.D.