no. 4
Fully commutative Kazhdan-Lusztig cells
[Cellules pleinement commutatives de Kazhdan-Lusztig]
Green, Richard M.1 ; Losonczy, Jozsef2
1 Lancaster University, Department of Mathematics and Statistics, Lancaster LA1 4YF (Grande-Bretagne)
2 Long Island University, Department of Mathematics, Brookville, NY 11548 (USA)
Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1025-1045.

Nous étudions la compatibilité entre l'ensemble des éléments pleinement commutatifs d'un groupe de Coxeter et les divers types de cellules de Kazhdan-Lusztig, en utilisant une base canonique pour une version généralisée de l'algèbre de Temperley-Lieb.

We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.

DOI : 10.5802/aif.1843
Classification : 20C08, 20F55
Keywords: canonical basis, cell theory, Coxeter group, Hecke algebra, Kazhdan-Lusztig basis, Temperley-Lieb algebra
Mot clés : base canonique, théorie des cellules, groupe de Coxeter, algèbre de Hecke, base de Kazhdan-Lusztig, algèbre de Temperley-Lieb
Green, Richard M. 1 ; Losonczy, Jozsef 2

1 Lancaster University, Department of Mathematics and Statistics, Lancaster LA1 4YF (Grande-Bretagne)
2 Long Island University, Department of Mathematics, Brookville, NY 11548 (USA) 
@article{AIF_2001__51_4_1025_0,
     author = {Green, Richard M. and Losonczy, Jozsef},
     title = {Fully commutative {Kazhdan-Lusztig} cells},
     journal = {Annales de l'Institut Fourier},
     pages = {1025--1045},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {51},
     number = {4},
     year = {2001},
     doi = {10.5802/aif.1843},
     mrnumber = {1849213},
     zbl = {1008.20036},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1843/}
}
TY  - JOUR
AU  - Green, Richard M.
AU  - Losonczy, Jozsef
TI  - Fully commutative Kazhdan-Lusztig cells
JO  - Annales de l'Institut Fourier
PY  - 2001
SP  - 1025
EP  - 1045
VL  - 51
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.1843/
DO  - 10.5802/aif.1843
LA  - en
ID  - AIF_2001__51_4_1025_0
ER  - 
%0 Journal Article
%A Green, Richard M.
%A Losonczy, Jozsef
%T Fully commutative Kazhdan-Lusztig cells
%J Annales de l'Institut Fourier
%D 2001
%P 1025-1045
%V 51
%N 4
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.1843/
%R 10.5802/aif.1843
%G en
%F AIF_2001__51_4_1025_0
Green, Richard M.; Losonczy, Jozsef. Fully commutative Kazhdan-Lusztig cells. Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1025-1045. doi : 10.5802/aif.1843. http://archive.numdam.org/articles/10.5802/aif.1843/

[1] F. du Cloux Coxeter Version 1.01, Université de Lyon, France, 1991

[2] C.K. Fan A Hecke algebra quotient and properties of commutative elements of a Weyl group (1995) (Ph.D. thesis, M.I.T.)

[3] C.K. Fan; R.M. Green Monomials and Temperley--Lieb algebras, J. Algebra, Volume 190 (1997), pp. 498-517 | DOI | MR | Zbl

[4] C.K. Fan; J.R. Stembridge Nilpotent orbits and commutative elements, J. Algebra, Volume 196 (1997), pp. 490-498 | DOI | MR | Zbl

[5] D. Garfinkle On the classification of primitive ideals for complex classical Lie algebras, I, Compositio Math., Volume 75 (1990), pp. 135-169 | Numdam | MR | Zbl

[6] D. Garfinkle On the classification of primitive ideals for complex classical Lie algebras, II, Compositio Math., Volume 81 (1992), pp. 307-336 | Numdam | MR | Zbl

[7] D. Garfinkle On the classification of primitive ideals for complex classical Lie algebras, III, Compositio Math., Volume 88 (1993), pp. 187-234 | Numdam | MR | Zbl

[8] J.J. Graham Modular representations of Hecke algebras and related algebras (1995) (Ph.D. thesis, University of Sydney)

[9] R.M. Green Generalized Temperley--Lieb algebras and decorated tangles, J. Knot Theory Ramifications, Volume 7 (1998), pp. 155-171 | DOI | MR | Zbl

[10] R.M. Green Decorated tangles and canonical bases (Preprint) | MR | Zbl

[11] R.M. Green; J. Losonczy Canonical bases for Hecke algebra quotients, Math. Res. Lett., Volume 6 (1999), pp. 213-222 | MR | Zbl

[12] R.M. Green; J. Losonczy A projection property for Kazhdan--Lusztig bases, Internat. Math. Res. Notices, Volume 1 (2000), pp. 23-34 | DOI | MR | Zbl

[13] J.E. Humphreys Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge, 1990 | MR | Zbl

[14] D. Kazhdan; G. Lusztig Representations of Coxeter groups and Hecke algebras, Invent. Math., Volume 53 (1979), pp. 165-184 | DOI | MR | Zbl

[15] J. Losonczy The Kazhdan--Lusztig basis and the Temperley--Lieb quotient in type D, J. Algebra, Volume 233 (2000), pp. 1-15 | DOI | MR | Zbl

[16] G. Lusztig Cells in affine Weyl groups, II, J. Algebra, Volume 109 (1987), pp. 536-548 | DOI | MR | Zbl

[17] J.R. Stembridge On the fully commutative elements of Coxeter groups, J. Algebraic Combin., Volume 5 (1996), pp. 353-385 | DOI | MR | Zbl

Cité par Sources :