Boundaries of K-types in discrete series
Massachusetts Institute of Technology. Dept. of Mathematics.
Michael J. Hopkins and David A. Vogan.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliographical references (p. 75-76).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology