TY - JOUR
T1 - Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers
AU - Tate, Tatsuya
AU - Zelditch, Steve
N1 - Funding Information:
·Corresponding author. E-mail addresses: tate@math.nagoya-u.ac.jp (T. Tate), zelditch@math.jhu.edu (S. Zelditch). 1Current address: Graduate School of Mathematics, Nagoya University, Chikusa-Ku, Nagoya, 464-8602 Japan. Research partially supported by JSPS. 2Research partially supported by NSF Grants DMS-0071358 DMS-0302518 and by the Clay Foundation.
PY - 2004/12/15
Y1 - 2004/12/15
N2 - 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.
AB - 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.
KW - Central limit region
KW - Lattice path with steps in a convex polytope
KW - Multiplicity of a weight or irreducible
KW - Strong deviations region
KW - Tensor power
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U2 - 10.1016/j.jfa.2004.01.004
DO - 10.1016/j.jfa.2004.01.004
M3 - Article
AN - SCOPUS:4344568478
SN - 0022-1236
VL - 217
SP - 402
EP - 447
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -