Séminaire Lotharingien de Combinatoire, B32c (1994), 38
pp.
J. Désarménien, B. Leclerc and J.-Y. Thibon
Hall-Littlewood Functions and Kostka-Foulkes Polynomials in Representation
Theory
Abstract.
This paper presents a survey of recent applications of
Hall-Littlewood functions and Kostka-Foulkes polynomials
to the representation theory of the general
linear group GL(n,C) and of the symmetric group S(n).
The reviewed topics include the q-analogue of Kostant's
partition function, vertex operators, generalized exponents
of GL(n,C) and S(n)-harmonic polynomials. We also give
a detailed description of the various combinatorial
interpretations of Kostka-Foulkes polynomials. We conclude
with the study of Hall-Littlewood functions at roots of
unity, which provide a combinatorial description of certain
plethysms.
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