q-Analogs of symmetric function operators

2000/08/24 by Mike Zabrocki, Zabrocki, Mike · 1 citation
Mathematics · #05E05 #Advanced Mathematical Identities #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Quantum Algebra (math.QA) #math.CO #math.QA #msc:05E05

paper · pdf · doi:10.48550/arxiv.math/0008188

17 pages - minor revisions to appear in Discrete Mathematics issue for LaCIM'2000

openalex publication_date 2000/08/24 · arxiv created 2002/01/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any homomorphism V on the space of symmetric functions, we introduce an operation which creates a q-analog of V. By giving several examples we demonstrate that this quantization occurs naturally within the theory of symmetric functions. In particular, we show that the Hall-Littlewood symmetric functions are formed by taking this q-analog of the Schur symmetric functions and the Macdonald symmetric functions appear by taking the q-analog of the Hall-Littlewood symmetric functions in the parameter t. This relation is then used to derive recurrences on the Macdonald q,t-Kostka coefficients.

Citations

• Ubiquity of Kostka polynomials

Cited by

• Constructing Hall-Littlewood Functions via a Deformation of the Bernstein Operator

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