Combinatorial extension of stable branching rules for classical groups

TL;DR

This paper introduces new combinatorial formulas for tensor product decompositions and branching rules of classical Lie algebra modules, extending stable rules to all highest weights using a spinor crystal model.

Contribution

It provides a novel combinatorial approach that generalizes stable branching rules for classical groups to arbitrary highest weights, including Littlewood restriction rules.

Findings

New combinatorial formulas for tensor product decompositions.

Extension of stable branching rules to all highest weights.

Bijective correspondence with classical crystal models.

Abstract

We give new combinatorial formulas for decomposition of the tensor product of integrable highest weight modules over the classical Lie algebras of type $B, C, D$, 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.