# Bihomogeneous symmetric functions

Speaker:

Yuly Billig, Carleton University

Date and Time:

Sunday, January 27, 2019 - 10:50am to 11:10am

Location:

University of Ottawa

Abstract:

The goal of this talk is to compute the spectrum of the second order differential operator $T = \frac{1}{2} \sum\limits_{a+b=c+d} x_a x_b \frac{\partial}{\partial x_c} \frac{\partial}{\partial x_d}$ acting on the Fock space $C[x_1, x_2, \ldots]$. This is done by interpreting the Fock space as a space of symmetric functions and considering two gradings on this space, by degree and by length. We construct a basis in the space of bihomogeneous symmetric functions and show that operator $T$ is triangular in this basis. This allows us to compute the eigenvalues of $T$, which turn out to be non-negative integers.