1,357 research outputs found
Cut-and-join structure and integrability for spin Hurwitz numbers
Spin Hurwitz numbers are related to characters of the Sergeev group, which
are the expansion coefficients of the Q Schur functions, depending on odd times
and on a subset of all Young diagrams. These characters involve two dual
subsets: the odd partitions (OP) and the strict partitions (SP). The Q Schur
functions Q_R with R\in SP are common eigenfunctions of cut-and-join operators
W_\Delta with \Delta\in OP. The eigenvalues of these operators are the
generalized Sergeev characters, their algebra is isomorphic to the algebra of Q
Schur functions. Similarly to the case of the ordinary Hurwitz numbers, the
generating function of spin Hurwitz numbers is a \tau-function of an integrable
hierarchy, that is, of the BKP type. At last, we discuss relations of the
Sergeev characters with matrix models.Comment: 22 page
Linear versus spin: representation theory of the symmetric groups
We relate the linear asymptotic representation theory of the symmetric groups
to its spin counterpart. In particular, we give explicit formulas which express
the normalized irreducible spin characters evaluated on a strict partition
with analogous normalized linear characters evaluated on the double
partition . We also relate some natural filtration on the usual
(linear) Kerov-Olshanski algebra of polynomial functions on the set of Young
diagrams with its spin counterpart. Finally, we give a spin counterpart to
Stanley formula for the characters of the symmetric groups.Comment: 41 pages. Version 2: new text about non-oriented (but orientable)
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