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Article overview
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Plethysms, replicated Schur functions and series, with applications to vertex operators | | Bertfried Fauser
; Peter D Jarvis
; Ronald C King
; | | Date: |
22 Jun 2010 | | Abstract: | Specializations of Schur functions are exploited to define and evaluate the
Schur functions s_lambda[alpha X] and plethysms s_lambda[alpha s_
u(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_lambda^{(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^perp dual to L_sigma, and then more explicitly in exponential form.
Finally the replicated form of such vertex operators are written down. | | Source: | arXiv, 1006.4266 | | Services: | Forum | Review | PDF | Favorites | |
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