Macdonald symmetric functions of rectangular shapes

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.

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

References in corpus (3)

• Jack vertex operators and realization of Jack functions
• A generalization of Newton's identity and Macdonald functions
• Constant term identities and Poincare polynomials