Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers |
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Authors: | Tatsuya Tate Steve Zelditch |
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Affiliation: | a Department of Mathematics, Keio University, 3-14-1 Hiyoshi Kohoku-ku, Yokohama 223-8522, Japan b Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA |
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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. |
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Keywords: | Multiplicity of a weight or irreducible Tensor power Lattice path with steps in a convex polytope Central limit region Strong deviations region |
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