Paper detail

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

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.