Comptes Rendus
no. 3-4
Lie Algebras
The t-analog of the level one string function for twisted affine Kac–Moody algebras

Presented by: the Editorial Board

Sachin S. Sharma1; Sankaran Viswanath1
1 The Institute of Mathematical Sciences, CIT campus, Taramani, Chennai 600113, India
Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 133-136.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.01.021

Sachin S. Sharma 1; Sankaran Viswanath 1

1 The Institute of Mathematical Sciences, CIT campus, Taramani, Chennai 600113, India 
@article{CRMATH_2012__350_3-4_133_0,
     author = {Sachin S. Sharma and Sankaran Viswanath},
     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},
}
TY  - JOUR
AU  - Sachin S. Sharma
AU  - Sankaran Viswanath
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
DO  - 10.1016/j.crma.2012.01.021
LA  - en
ID  - CRMATH_2012__350_3-4_133_0
ER  - 
%0 Journal Article
%A Sachin S. Sharma
%A Sankaran Viswanath
%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
%R 10.1016/j.crma.2012.01.021
%G en
%F CRMATH_2012__350_3-4_133_0
Sachin S. Sharma; Sankaran Viswanath. The t-analog of the level one string function for twisted affine Kac–Moody algebras. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 133-136. doi : 10.1016/j.crma.2012.01.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.021/

[1] R.K. Brylinski Limits of weight spaces, Lusztigʼs q-analogs, and fiberings of adjoint orbits, J. Amer. Math. Soc., Volume 2 (1989) no. 3, pp. 517-533

[2] S. Fishel; I. Grojnowski; C. Teleman The strong Macdonald conjecture and Hodge theory on the loop Grassmannian, Ann. of Math. (2), Volume 168 (2008) no. 1, pp. 175-220

[3] B. Ion The Cherednik kernel and generalized exponents, Int. Math. Res. Not., Volume 36 (2004), pp. 1869-1895

[4] V.G. Kac Infinite Dimensional Lie Algebras, Cambridge University Press, 1990

[5] V.G. Kac; D.H. Peterson Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. Math., Volume 53 (1984) no. 2, pp. 125-264

[6] B. Kostant The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math., Volume 81 (1959), pp. 973-1032

[7] W. Slofstra A Brylinski filtration for affine Kac–Moody algebras, Adv. Math., Volume 229 (2012) no. 2, pp. 968-983

[8] S. Viswanath Kostka–Foulkes polynomials for symmetrizable Kac–Moody algebras, Sém. Lothar. Combin., Volume 58 (2008) (Art. B58f)

Cited by Sources:

Comments - Policy