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

Bertfried Fauser, PD Jarvis, RC King

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Specializations of Schur functions are exploited to define and evaluate the Schur functions s(lambda)[alpha X] and plethysms s(lambda)[as(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(pi)((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(perpendicular to) dual to L-sigma, and then more explicitly in the exponential form. Finally the replicated form of such vertex operators are written down.
Original languageEnglish
Pages (from-to)405202
Number of pages1
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number40
DOIs
Publication statusPublished - 8 Oct 2010

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