2008/05/24 by A. Gerasimov, Anton Gerasimov, Gerasimov, Anton +4
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical functions and polynomials #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.0805.3754
20 pages, several typos corrected
openalex publication_date 2008/05/24 · arxiv created 2008/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We identify q-deformed gl(l+1)-Whittaker functions with a specialization of Macdonald polynomials. This provides a representation of q-deformed gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie algebra gl(l+1). We also define a system of dual Hamiltonians for q-deformed gl(l+1)-Toda chains and give a new integral representation for q-deformed gl(l+1)-Whittaker functions. Finally an expression of q-deformed gl(l+1)-Whittaker function as a matrix element of a quantum torus algebra is derived.