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Flagged Littlewood-Richardson tableaux and branching rule for classical groups (1908.11041v2)
Published 29 Aug 2019 in math.RT, math.CO, and math.QA
Abstract: We give a new formula for the branching rule from ${\rm GL}n$ to ${\rm O}_n$ generalizing the Littlewood's restriction formula. The formula is given in terms of Littlewood-Richardson tableaux with certain flag conditions which vanish in a stable range. As an application, we give a combinatorial formula for the Lusztig $t$-weight multiplicity $K{\mu 0}(t)$ of type $B_n$ and $D_n$ with highest weight $\mu$ and weight $0$.
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