Plethysms, replicated Schur functions and series, with applications to vertex operators
arXiv:1006.4266 · doi:10.1088/1751-8113/43/40/405202
Abstract
Specializations of Schur functions are exploited to define and evaluate the Schur functions s_λ[αX] and plethysms s_λ[αs_ν(X))] for any α- integer, real or complex. Plethysms are then used to define pairs of mutually inverse infinite series of Schur functions, M_πand L_π, specified by arbitrary partitions π. These are used in turn to define and provide generating functions for formal characters, s_λ^{(π)}, of certain groups H_π, 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_σ^\perp dual to L_σ, and then more explicitly in exponential form. Finally the replicated form of such vertex operators are written down.
36 pages, uses youngtab.tex
References in corpus (4)
Cited by in corpus (10)
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