Speaker
Florian Schreier-Aigner, University of Vienna
Abstract
“There is a rich and well-studied combinatorial theory associated with Schur polynomials including several correspondences such as the Robinson-Schensted-Knuth correspondence (RSK) and the Bender-Knuth involution. Over the last 1.5 decades there was a strong focus on lifting RSK and its variants to Macdonald polynomials with a complete success for the intermediate levels of q-Whittaker and Hall-Littlewood polynomials and partial success for Macdonald polynomials. On the other hand, no similar development exists for generalising the Bender-Knuth involution for Macdonald polynomials.
In this talk, I show that we can lift an important connection from Schur polynomials to Macdonald polynomials, namely that the Bender-Knuth involution can be used to define the row-insertion RSK and vice versa.
The talk is based on work in progress together with Jerónimo Valencia Porras.”