Flagged Littlewood-Richardson tableaux and branching rule for classical groups

Abstract

We give a new formula for the branching rule from ${\mathrm{GL}}_n$ to ${\mathrm{O}}_n$ 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 $0$.

50 pages, revised introduction, reference added, Corollary 4.12 added, comments added on Remark 3.22, 4.15, 4.19 and 5.8, comments added for Sections 3 and 6, to appear in Journal of Combinatorial Theory, Series A

Cited by in corpus (3)

• Combinatorial Howe duality of symplectic type
• Based modules over the $ı$quantum group of type AI
• A new tableau model for irreducible polynomial representations of the orthogonal group