  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.
