Notes about the KP/BKP correspondence

A. Yu. Orlov

Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 416-439

Résumé

We present a set of remarks related to previous work. These are remarks on polynomials solutions, the application of the Wick theorem, examples of creation of polynomial solutions with the help of vertex operators, the eigenproblem for polynomials, and a remark on the conjecture by Alexandrov and Mironov, Morozov about the ratios of the projective Schur functions. New results on the bilinear relations between characters of the symmetric group and the Sergeev group and on bilinear relations between skew Schur and projective Schur functions and also between shifted Schur and projective Schur functions are added. Certain new matrix models are discussed.

Détail

Keywords: KP tau function, BKP tau function, Schur function, projective Schur function, shifted Schur function, character of symmetric group, character of Sergeev group, symmetric polynomial, vertex operator, eigenvalue problem.

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