An elliptic hypergeometric function approach to branching rules. (English) Zbl 1462.05351
Summary: We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose some conjectural branching rules and allied conjectures exhibiting a novel type of vanishing behaviour involving partitions with empty 2-cores.
MSC:
| 05E05 | Symmetric functions and generalizations |
| 05E10 | Combinatorial aspects of representation theory |
| 20C33 | Representations of finite groups of Lie type |
| 33D05 | \(q\)-gamma functions, \(q\)-beta functions and integrals |
| 33D52 | Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) |
| 33D67 | Basic hypergeometric functions associated with root systems |
Keywords:
branching formulas; elliptic hypergeometric series; elliptic Selberg integrals; interpolation functions; Koornwinder polynomials; Littlewood identities; Macdonald polynomialsReferences:
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