Speaker: John Harnad (Concordia University, Mathematical Physics Lab, Centre de recherches mathématiques)

Title: Bilinear expansions of lattices of KP τ-function in BKP τ-functions: a fermionic approach

Abstract: The notion of Kadomtsev-Petviashvili (KP) and BKP τ- functions will be recalled, together with their representations as fermionic expectation values. Schur-type lattices of such KP and BKP τ-functions will be defined, corresponding to a given infinite general linear or orthogonal group element, labelled by partitions and strict partitions respectively. A bilinear expansion expressing elements of these lattices of KP τ-functions as sums over products of pairs of elements of associated lattices of BKP τ-functions  will be presented, generalizing earlier results relating determinants and Pfaffians of minors of  skew symmetric matrices, with applications to Schur functions and Schur Q-functions. Further applications include inhomogeneous polynomial τ-functions of KP and BKP type, with their determinantal and Pfaffian representations.