### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Generalized Adjoint Actions and Combinatorics

Speaker: **Vladimir Retakh**, Rutgers University

Date: Thursday, October 22, 2015 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

There is a classical formula expressing adjoint action exp(x)yexp(-x) for noncommuting variables x and y as an infinite sum of iterated brackets [x,...,[x,y]...]. We replace exp(x) by any formal series f(x) and show that the result can be written as an infinite sum of generalized iterated brackets. To describe the generalized brackets we need a special class of Hall-Littlewood polynomials. I am going to discuss various combinatorial properties of these polynomials. This is a joint paper with A. Berenstein (U. of Oregon)

See: http://www.math.rutgers.edu/~russell2/expmath/