Littlewood-Richardson coefficients describe the decomposition of tensor products of irreducible representations of a simple Lie algebra into irreducibles. Assuming the number of factors is large, one gets a measure on the space of weights. This limiting measure was extensively studied by many authors. In particular, Kerov computed the corresponding density in a special case in type A and Kuperberg gave a formula for the general case. The goal of this paper is to give a short, self-contained and pure Lie theoretic proof of the formula for the density of the limiting measure. Our approach is based on the link between the limiting measure induced by the Littlewood-Richardson coefficients and the measure defined by the weight multiplicities of the tensor products.
1
Department of Mathematics, HSE University, Moscow 119048, Russia
2
Skolkovo Institute of Science and Technology, Moscow 143026, Russia
Evgeny Feigin. Large Tensor Products and Littlewood-Richardson Coefficients. Journal of Lie Theory, Tome 29 (2019) no. 4, pp. 927-940. http://geodesic.mathdoc.fr/item/JOLT_2019_29_4_a1/
@article{JOLT_2019_29_4_a1,
author = {Evgeny Feigin},
title = {Large {Tensor} {Products} and {Littlewood-Richardson} {Coefficients}},
journal = {Journal of Lie Theory},
pages = {927--940},
year = {2019},
volume = {29},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_4_a1/}
}
TY - JOUR
AU - Evgeny Feigin
TI - Large Tensor Products and Littlewood-Richardson Coefficients
JO - Journal of Lie Theory
PY - 2019
SP - 927
EP - 940
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2019_29_4_a1/
ID - JOLT_2019_29_4_a1
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