An elliptic hypergeometric function approach to branching rules
DOI10.3842/SIGMA.2020.142zbMath1462.05351arXiv2007.03174OpenAlexW3040613977MaRDI QIDQ2024528
Eric M. Rains, S. Ole Warnaar, Chul-Hee Lee
Publication date: 4 May 2021
Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.03174
interpolation functionsMacdonald polynomialsKoornwinder polynomialselliptic hypergeometric seriesLittlewood identitieselliptic Selberg integralsbranching formulas
Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) (q)-gamma functions, (q)-beta functions and integrals (33D05) Representations of finite groups of Lie type (20C33) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Basic hypergeometric functions associated with root systems (33D67)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Elliptic Littlewood identities
- Derivation of a \(BC_n\) elliptic summation formula via the fundamental invariants
- Branching rules for symmetric functions and \(\mathfrak{sl}_n\) basic hypergeometric series
- Pieri formulas for Macdonald's spherical functions and polynomials
- Branching rules for symmetric hypergeometric polynomials
- Branching formula for Macdonald-Koornwinder polynomials
- \(BC_n\)-symmetric abelian functions
- Transformations of elliptic hypergeometric integrals
- Limits of elliptic hypergeometric integrals
- Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)
- \(BC\)-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials
- Applications of minor summation formulas to rectangular-shaped representations of classical groups
- Identities for classical group characters of nearly rectangular shape
- Extensions of the well-poised and elliptic well-poised Bailey lemma
- Transformation formulas for multivariable basic hypergeometric series
- Orthogonal polynomials associated with root systems
- Macdonald polynomials of type \(C_n\) with one-column diagrams and deformed Catalan numbers
- Multivariate quadratic transformations and the interpolation kernel
- An approach to the branching rule from \(\mathfrak{sl}_{2n}(\mathbb C)\) to \(\mathfrak{sp}_{2n}(\mathbb C)\) via Littelmann's path model
- A duality of MacDonald-Koornwinder polynomials and its application to integral representations
- Summation and transformation formulas for elliptic hypergeometric series.
- Branching rules for Koornwinder polynomials with one column diagrams and matrix inversions
- Multidimensional matrix inversions and elliptic hypergeometric series on root systems
- AFLT-type Selberg integrals
- Vanishing integrals of Macdonald and Koornwinder polynomials
- A conjecture about raising operators for Macdonald polynomials
- BC\(_n\)-symmetric polynomials
- On the elliptic beta function
- A generalization of Selberg’s beta integral
- Shifted Plane Partitions of Trapezoidal Shape
- Branching rules for classical Lie groups using tensor and spinor methods
- On q-Analogues of the Watson and Whipple Summations
- First order analytic difference equations and integrable quantum systems
- A non-levi branching rule in terms of Littelmann paths
- Combinatorial extension of stable branching rules for classical groups
- Summation formulae for elliptic hypergeometric series
- The poset of $k$-shapes and branching rules for $k$-Schur functions
- Bounded Littlewood identities
- An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums
- Change of base in Bailey pairs