Abstract: 
Motivated by the striking resemblance between an identity of Klyachko from 1985 and Macdonald's reduced word identity from 1991, I will discuss what we call the q-Klyachko algebra. It is a commutative
algebra with a simple presentation and a basis of squarefree monomials, whose combinatorics interplay nicely with many classical families of multivariate polynomials. My focus will largely be on a q-analog of Postnikov's mixed Eulerian numbers that arises naturally as coefficients in this algebra. I will interpret this new family of polynomials from a probabilistic point of view, and explain some of its combinatorial  properties. I will conclude with a simultaneous generalization of the aforementioned identities of Klyachko and Macdonald, and discuss some applications.

This is joint work with Vasu Tewari (University of Hawai'i).

https://zoom.us/j/94541219182?pwd=ZDdOT1poNUxTNlBFUE93M1dIZ0Eydz09

Meeting-ID: 945 4121 9182
Kenncode: Let2Vh