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SUMMARY:John Harnad (CRM & Concordia University)
DTSTART:20211022T010000Z
DTEND:20211022T020000Z
DTSTAMP:20260423T024534Z
UID:CGP-MP/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CGP-MP/17/">
 Bilinear expansions of lattices of KP $\\tau$-functions in BKP $\\tau$-fun
 ctions\, determinant and Pfaffian expressions of polynomial $\\tau$-functi
 ons</a>\nby John Harnad (CRM & Concordia University) as part of IBS-CGP Ma
 thematical Physics Seminar\n\n\nAbstract\nThe notion of Kadomtsev-Petviash
 vili (KP) and BKP $\\tau$ functions will\nbe recalled\, together with thei
 r representations as fermionic expectation values.\nSchur-type lattices of
  KP and BKP $\\tau$-functions will be defined\, corresponding to\na given 
 infinite general linear or orthogonal group element\, labelled by partitio
 ns\nand strict partitions respectively. A bilinear expansion expressing el
 ements of these lattices of KP $\\tau$-functions\nas sums over products of
  pairs of elements of associated lattices of BKP $\\tau$-functions  will b
 e presented\,\ngeneralizing earlier results relating determinants and Pfaf
 fians of minors of  skew symmetric matrices\,\nwith applications to Schur 
 functions and Schur $Q$-functions. Further applications include\ndetermina
 ntal and Pfaffian representations of all inhomogeneous polynomial $\\tau$-
 functions of KP and BKP type.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/17/
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