An invitation to wreath Macdonald polynomials

Abstract: Macdonald polynomials are distinguished symmetric functions that have played important or useful roles in a wide range of fields: combinatorics, enumerative geometry, integrable systems, probability, knot theory, etc. Defined by Haiman, wreath Macdonald polynomials are generalizations of Macdonald polynomials wherein the symmetric groups are replaced with their wreath products with a fixed cyclic group Z/rZ. I will discuss work in progress where, using the quantum toroidal algebra of rank r, one can derive analogues of some standard parts of Macdonald theory: orthogonality, evaluation formulas, and difference operators. This is joint work with Daniel Orr and Mark Shimozono.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides )

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections