Adding ± 1 to the argument of an Hall-Littlewood polynomial

2007/09/13 by Alain Lascoux, Lascoux, Alain
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.0709.2088

arxiv created 2007/09/13 · arxiv updated 2009/12/01

Abstract

Shifting by ± 1 powers sums: p_i → p_i ± 1 induces a transformation on symmetric functions that we detail in the case of Hall-Littlewood polynomials. By iteration, this gives a description of these polynomials in terms of plane partitions, as well as some generating functions. We recover in particular an identity of Warnaar related to Rogers-Ramanujan identities.

Related

• New Identities of Hall-Littlewood Polynomials and Rogers-Ramanujan Type
• On Hall-Littlewood polynomials
• Generalized Andrews-Gordon Identities
• On a family of symmetric rational functions
• Refined Littlewood identity for spin Hall-Littlewood symmetric rational functions