Séminaire Lotharingien de Combinatoire, 85B.52 (2021), 12 pp.

Mrigendra Singh Kushwaha, K. N. Raghavan and Sankaran Viswanath

The saturation Problem for Refined Littlewood-Richardson Coefficients

Abstract. Given partitions λ, μ, ν with at most n nonzero parts and a permutation wSn, the refined Littlewood-Richardson coefficient cλμν(w) is the multiplicity of the irreducible GLnC module V(ν) in the so-called Kostant-Kumar submodule K(λ,w,μ) of the tensor product V(λ) ⊗ V(μ). We derive a hive model for these coefficients and prove that the saturation property holds if w is 312-avoiding, 231-avoiding or a commuting product of such elements. This generalizes the classical Knutson-Tao saturation theorem.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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