Bilinear expansions of lattices of KP $\tau$-functions in BKP $\tau$-functions, determinant and Pfaffian expressions of polynomial $\tau$-functions

Abstract: The notion of Kadomtsev-Petviashvili (KP) and BKP $\tau$ functions will be recalled, together with their representations as fermionic expectation values. Schur-type lattices of KP and BKP $\tau$-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 $\tau$-functions as sums over products of pairs of elements of associated lattices of BKP $\tau$-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 determinantal and Pfaffian representations of all inhomogeneous polynomial $\tau$-functions of KP and BKP type.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration