[Le t-analogue de la fonction corde de niveau un pour les algèbres de Kac–Moody affines tordues]
On étudie le t-analogue, dʼaprès Lusztig, des multiplicités des poids, cʼest-à-dire les polynômes de Kostka–Foulkes affines, associés aux représentations du niveau un des algèbres de Kac–Moody affines tordues. On obtient une expression explicite pour lʼunique t-fonction de corde, en utilisant les identités de Macdonald et Cherednik. Cela étend des travaux précédents sur les t-fonctions de corde pour les algèbres de Kac–Moody affines non-tordues de type A-D-E.
We study Lusztigʼs t-analog of weight multiplicities, or affine Kostka–Foulkes polynomials, associated to level one representations of twisted affine Kac–Moody algebras. We obtain an explicit closed form expression for the unique t-string function, using constant term identities of Macdonald and Cherednik. This extends previous work on t-string functions for the untwisted simply-laced affine Kac–Moody algebras.
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@article{CRMATH_2012__350_3-4_133_0,
author = {Sharma, Sachin S. and Viswanath, Sankaran},
title = {The \protect\emph{t}-analog of the level one string function for twisted affine {Kac{\textendash}Moody} algebras},
journal = {Comptes Rendus. Math\'ematique},
pages = {133--136},
publisher = {Elsevier},
volume = {350},
number = {3-4},
year = {2012},
doi = {10.1016/j.crma.2012.01.021},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.01.021/}
}
TY - JOUR AU - Sharma, Sachin S. AU - Viswanath, Sankaran TI - The t-analog of the level one string function for twisted affine Kac–Moody algebras JO - Comptes Rendus. Mathématique PY - 2012 SP - 133 EP - 136 VL - 350 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.01.021/ DO - 10.1016/j.crma.2012.01.021 LA - en ID - CRMATH_2012__350_3-4_133_0 ER -
%0 Journal Article %A Sharma, Sachin S. %A Viswanath, Sankaran %T The t-analog of the level one string function for twisted affine Kac–Moody algebras %J Comptes Rendus. Mathématique %D 2012 %P 133-136 %V 350 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.01.021/ %R 10.1016/j.crma.2012.01.021 %G en %F CRMATH_2012__350_3-4_133_0
Sharma, Sachin S.; Viswanath, Sankaran. The t-analog of the level one string function for twisted affine Kac–Moody algebras. Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 133-136. doi : 10.1016/j.crma.2012.01.021. http://www.numdam.org/articles/10.1016/j.crma.2012.01.021/
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