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

By T. Tate, Steve Zelditch. 2003

47 citations recorded by the source corpus.

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V #N l of an irreducible representation Vl 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. r 2004 Published by Elsevier Inc.

Subfields: Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bf1b1bb9ebe01515a372a08ed7f1c68ab01a660e