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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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