An Elliptic Hypergeometric Function Approach to Branching Rules

Abstract

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.

References in corpus (15)

• Summation and transformation formulas for elliptic hypergeometric series
• Orthogonal polynomials associated with root systems
• Multivariate Quadratic Transformations and the Interpolation Kernel
• A direct approach to the bispectral problem for the Ruijsenaars-Macdonald q-difference operators
• A Conjecture about Raising Operators for Macdonald Polynomials
• A non-Levi branching rule in terms of Littelmann paths
• Elliptic hypergeometric functions associated with root systems
• AFLT-type Selberg integrals
• Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
• Derivation of a $B{C}_n$ elliptic summation formula via the fundamental invariants
• Branching Formula for Macdonald-Koornwinder Polynomials
• Branching Rules for Symmetric Hypergeometric Polynomials
• Branching Rules for Koornwinder Polynomials with One Column Diagrams and Matrix Inversions
• Macdonald Polynomials of Type $C_n$ with One-Column Diagrams and Deformed Catalan Numbers
• Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series

Cited by in corpus (5)

• Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation
• Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
• Skew odd orthogonal characters and interpolating Schur polynomials
• Universal characters twisted by roots of unity
• Proof of some Littlewood identities conjectured by Lee, Rains and Warnaar