A centerless representation of the Virasoro algebra associated with the unitary circular ensemble

Luc Haine, Didier Vanderstichelen

We consider the 2-dimensional Toda lattice tau functions ${\tau }_n(t,s;\eta ,\theta )$ deforming the probabilities ${\tau }_n(\eta ,\theta )$ that a randomly chosen matrix from the unitary group U(n), for the Ha…