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

2010/06/22 by Bertfried Fauser, Peter D Jarvis, Ronald C King · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.RA #msc:05E05 #msc:17B69 #msc:11E57 #msc:16W30 #msc:20E22 #msc:33D52

paper · pdf · doi:10.1088/1751-8113/43/40/405202

published as J. Phys. A. Math and Theor. Vol 43, 2010, 405201 · 36 pages, uses youngtab.tex

arxiv created 2010/06/22 · arxiv updated 2010/09/14

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^⊥ dual to L_σ, and then more explicitly in exponential form. Finally the replicated form of such vertex operators are written down.

Cited by

• Elliptic Genera and q-Series Development in Analysis, String Theory, and N=2 Superconformal Field Theory
• S-Functions, Spectral Functions of Hyperbolic Geometry, and Vertex Operators with Applications to Structure for Weyl and Orthogonal Group Invariants

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