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arXiv · 1006.4266

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

Bertfried Fauser·Peter D Jarvis·Ronald C King
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Abstract

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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Bertfried Fauser, Peter D Jarvis, Ronald C King. 2010-06-22. Plethysms, replicated Schur functions and series, with applications to vertex operators. https://doi.org/10.1088/1751-8113/43/40/405202

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