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

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

2003-05-17

arxiv.org/abs/math/0305251v1

J. Funct. Anal. 217 (2004), no. 2, 402--447.

Mathematics

Representation Theory

38 pages, no figures

Scientific paper

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers $V_{\lambda}^{\otimes N}$ of an irreducible representation $V_{\lambda}$ 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.

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