English

Symmetric function generalizations of the $q$-Baker--Forrester ex-conjecture and Selberg-type integrals

Combinatorics 2022-10-26 v1

Abstract

It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the qq-Morris constant term identity. This conjecture was proved and extended by K\'{a}rolyi, Nagy, Petrov and Volkov in 2015. In this paper, we obtain two symmetric function generalizations of the qq-Baker--Forrester ex-conjecture. These includes: (i) a qq-Baker--Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV's result.

Keywords

Cite

@article{arxiv.2210.13469,
  title  = {Symmetric function generalizations of the $q$-Baker--Forrester ex-conjecture and Selberg-type integrals},
  author = {Guoce Xin and Yue Zhou},
  journal= {arXiv preprint arXiv:2210.13469},
  year   = {2022}
}

Comments

63 pages. arXiv admin note: text overlap with arXiv:2210.13245