Boundaries of K-types in discrete series
Name
261345009-MIT.pdf
Description
Full printable version
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3.12 MB
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Checksum (MD5)
f2c2443eeb8da1e5cfa2a6766224d59d
Author(s)
Havlíčková, Markéta
Advisor(s)
Michael J. Hopkins and David A. Vogan.
Date Issued
2008
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
Includes bibliographical references (p. 75-76).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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