An Elliptic Hypergeometric Function Approach to Branching Rules

被引：2

作者：

Lee, Chul-hee ^{[1
]}

Rains, Eric M. ^{[2
]}

Warnaar, S. Ole ^{[3
]}

机构：

[1] Korea Inst Adv Study, Sch Math, Seoul 02455, South Korea

[2] CALTECH, Dept Math, Pasadena, CA 91125 USA

[3] Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2020年 / 16卷

基金：

澳大利亚研究理事会;

关键词：

branching formulas; elliptic hypergeometric series; elliptic Selberg integrals; interpolation functions; Koornwinder polynomials; Littlewood identities; Macdonald polynomials; SUMMATION FORMULAS; MACDONALD; CONJECTURE;

D O I：

10.3842/SIGMA.2020.142

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：52

共 32 条

[1] Branching rules for symmetric hypergeometric polynomials
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