Notes about KP/BKP correspondence

Abstract

I present a set of remarks related to joint works \cite{paper1},\cite{paper2},\cite{paper3},\cite{MMNO}. These are remarks about polynomials solutions and vertex operators, eigenproblem for polynomials and a remark related to the the conjecture of Alexandrov and Mironov, Morozov about the ratios of the projective Schur functions. New results on the bilinear relations between characters of the symmetric and of 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 considered and a comment on Mironov-Morozov-Natanzon cut-and-join relation is added.

arXiv commentThe work is accepted by Theoretical and Mathematical Physics. A number of misprints is removed. Some notations are changed. The list of references is reordered

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• Connection between cut-and-join and Casimir operators
• Spin Hurwitz theory and Miwa transform for the Schur Q-functions