Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

Tatsuya Tate, Steve Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers Vλ ⊗N of an irreducible representation Vλ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.

Original languageEnglish (US)
Pages (from-to)402-447
Number of pages46
JournalJournal of Functional Analysis
Volume217
Issue number2
DOIs
StatePublished - Dec 15 2004

Keywords

  • Central limit region
  • Lattice path with steps in a convex polytope
  • Multiplicity of a weight or irreducible
  • Strong deviations region
  • Tensor power

ASJC Scopus subject areas

  • Analysis

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