A Survey of $q$-Whittaker polynomials

Abstract

Exploiting the fact that the $q$-Whittaker polynomials arise as a specialization of the (modified) Macdonald polynomials, we derive some of their basic properties, and explore interesting identities that they satisfy. We also show how they arise as graded Frobenius characteristics of ${\S }_n$-modules, and give a combinatorial approach to associated Pieri formulas.

arXiv comment29 pages, 12 figures

References in corpus (5)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Lattice Diagram Polynomials and Extended Pieri Rules
• Science Fiction and Macdonald's Polynomials
• Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups
• (GL_k x S_n)-modules and nabla of hook-indexed Schur functions