Stable branching rules for classical symmetric pairs

By Roger E. Howe, Eng-Chye Tan, Jeb F. Willenbring. 2003

139 citations recorded by the source corpus.

We approach the problem of obtaining branching rules from the point of view of dual reductive pairs. Specifically, we obtain a stable branching rule for each of 10 classical families of symmetric pairs. In each case, the branching multiplicities are expressed in terms of Littlewood-Richardson coefficients. Some of the formulas are classical and include, for example, Littlewood's restriction rule as a special case.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dd5a8c8f76fbe30d60ec2f1e17b4b65eb4812c64

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

• Tensor Representations of Classical Locally Finite Lie Algebras (2007, unknown): “ regarded as an sp ∞-module, therefore soc(r) Γ λ;0 = Γλ;0 ∩ soc (r) V⊗d. It is known that for any partitions λ,µ we have [Γ(2n) λ : Γ (n) hµi ] = P γ N λ µ,(2γ)⊤ provided n is large enough, see e.g. [HTW]. This implies that [Γλ;0 : Γhµi] = P γ N λ µ,(2γ)⊤, and combining it with the description of t”
• STABILITY PATTERNS IN REPRESENTATION THEORY (2013, methodology): “perty, or by restricting along an appropriate embedding GL →G. They are discussed in (7.10). The corresponding branching rules for all of these functors have been classically studied, and we refer to [HTW] for these rules. All of the rules follow the same pattern: they are sums over products of Litt”