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SUMMARY:John Harnad (Université de Montréal)
DTSTART:20210507T010000Z
DTEND:20210507T020000Z
DTSTAMP:20260423T024516Z
UID:CGP-MP/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CGP-MP/9/">B
 ilinear expansions of lattices of KP $\\tau$-function in BKP $\\tau$-funct
 ions: a fermionic approach</a>\nby John Harnad (Université de Montréal) 
 as part of IBS-CGP Mathematical Physics Seminar\n\n\nAbstract\nThe notion 
 of Kadomtsev-Petviashvili (KP) and BKP $\\tau$ functions will\nbe recalled
 \, together with their representations as fermionic expectation values.\nS
 chur-type lattices of such KP and BKP $\\tau$-functions will be defined\, 
 corresponding to\na given infinite general linear or orthogonal group elem
 ent\, labelled by partitions\nand strict partitions respectively. A biline
 ar 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 relati
 ng determinants and Pfaffians of minors of  skew symmetric matrices\, with
  applications to Schur functions and Schur $Q$-functions. Further applicat
 ions include inhomogeneous polynomial $\\tau$-functions of KP and BKP type
 \, with their determinantal and Pfaffian representations.\n\nRefs:\n 1) F.
  Balogh\, J. Harnad and J. Hurtubise\, “Isotropic Grassmannians\, Plück
 er and Cartan maps”\, J. Math. Phys. 62\, 021701 (2021)\n2) J. Harnad an
 d A. Yu. Orlov\, “Bilinear expansions of lattices of KP tau-functions in
  BKP tau-functions: a fermionic approach”\, J. Math. Phys. 62\, 013508 (
 2021)\n3) J. Harnad and A. Yu. Orlov\, “Bilinear expansions of Schur fun
 ctions in Schur Q-functions: a fermionic approach”\,  arxiv: 2008.13734 
 (Proc. Amer. Math. Soc.\, in press\, 2021)\n4) J. Harnad and A. Yu. Orlov\
 , “Polynomial KP and BKP τ-functions and correlators”\,  arXiv:2011.1
 3339\, (Ann. H. Poincaré\, in press 2021).\n
LOCATION:https://researchseminars.org/talk/CGP-MP/9/
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