Combinatorial extension of stable branching rules for classical groups. (English) Zbl 1430.17047
Summary: 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.
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 05E10 | Combinatorial aspects of representation theory |
| 20G05 | Representation theory for linear algebraic groups |
| 22E46 | Semisimple Lie groups and their representations |
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