Beschreibung:
Specializations of Schur functions are exploited to define and evaluate the Schur functions sl [aX] and plethysms sl [asv(X))] for any a-integer, real or complex. Plethysms are then used to define pairs of mutually inverse infinite series of Schur functions, Mp and Lp, specified by arbitrary partitions p. These are used in turn to define and provide generating functions for formal characters, s a,p, of certain groups Hp, 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 |s dual to Ls, and then more explicitly in exponential form. Finally the replicated form of such vertex operators are written down.