Plethysms, replicated Schur functions and series, with applications to vertex operators

Details Plethysms, replicated Schur functions and series, with applications to vertex operators Plethysms, replicated Schur functions and series, with applications to vertex operators

2010-06-22

arxiv.org/abs/1006.4266v1

J. Phys. A. Math and Theor. Vol 43, 2010, 405201

Physics

Mathematical Physics

36 pages, uses youngtab.tex

Scientific paper

10.1088/1751-8113/43/40/405202

Specializations of Schur functions are exploited to define and evaluate the Schur functions s_\lambda[\alpha X] and plethysms s_\lambda[\alpha s_\nu(X))] for any \alpha - integer, real or complex. Plethysms are then used to define pairs of mutually inverse infinite series of Schur functions, M_\pi and L_\pi, specified by arbitrary partitions \pi. These are used in turn to define and provide generating functions for formal characters, s_\lambda^{(\pi)}, of certain groups H_\pi, thereby extending known results for orthogonal and symplectic group characters. Each of these formal characters is then given a vertex operator realization, first in terms of the series M=M_{(0)} and various L_\sigma^\perp dual to L_\sigma, and then more explicitly in exponential form. Finally the replicated form of such vertex operators are written down.

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