An algebra of Klyachko, and (re)mixed Eulerian numbers

04.05.2021 15:15 - 16:45

Philippe Nadeau (CNRS, Universite Lyon-1)

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).

Meeting-ID: 945 4121 9182
Kenncode: Let2Vh


Ch. Krattenthaler

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