English

Macdonald symmetric functions of rectangular shapes

Combinatorics 2013-08-20 v1

Abstract

Using vertex operator we study Macdonald symmetric functions of rectangular shapes and their connection with the q-Dyson Laurent polynomial. We find a vertex operator realization of Macdonald functions and thus give a generalized Frobenius formula for them. As byproducts of the realization, we find a q-Dyson constant term orthogonality relation which generalizes a conjecture due to Kadell in 2000, and we generalize Matsumoto's hyperdeterminant formula for rectangular Jack functions to Macdonald functions.

Keywords

Cite

@article{arxiv.1308.3821,
  title  = {Macdonald symmetric functions of rectangular shapes},
  author = {Tommy Wuxing Cai},
  journal= {arXiv preprint arXiv:1308.3821},
  year   = {2013}
}

Comments

25 pages, Main results reported on The 13th national Conference on Lie Algebra, Sichuan,China (July 22, 2013)

R2 v1 2026-06-22T01:10:56.159Z