Combinatorial extension of stable branching rules for classical groups

Kwon, Jae-Hoon

doi:10.1090/tran/7104

Combinatorial extension of stable branching rules for classical groups
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Trans. Amer. Math. Soc. 370 (2018), 6125-6152 Request permission

Abstract:

We give new combinatorial formulas for decomposition of the tensor product of integrable highest weight modules over the classical Lie algebras of types $B, C, D$, and the branching decomposition of an integrable highest weight module with respect to a maximal Levi subalgebra of type $A$. This formula is based on a combinatorial model of classical crystals called spinor model. We show that our formulas extend in a bijective way various stable branching rules for classical groups to arbitrary highest weights, including the Littlewood restriction rules.

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