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=12∑a+b=c+dxaxb∂∂xc∂∂xd acting on the Fock space C[x1,x2,…]. 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.