Geodesic
Hall-Littlewood Functions and Kostka-Foulkes Polynomials in Representation Theory
Séminaire lotharingien de combinatoire, Tome 32 (1994)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_1994_32_a2,
     author = {J. D\'esarm\'enien and B. Leclerc and J.-Y. Thibon},
     title = {Hall-Littlewood {Functions} and {Kostka-Foulkes} {Polynomials} in {Representation} {Theory}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {32},
     year = {1994},
     url = {http://geodesic.mathdoc.fr/item/SLC_1994_32_a2/}
}
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J. Désarménien; B. Leclerc; J.-Y. Thibon. Hall-Littlewood Functions and Kostka-Foulkes Polynomials in Representation Theory. Séminaire lotharingien de combinatoire, Tome 32 (1994). http://geodesic.mathdoc.fr/item/SLC_1994_32_a2/