Fully commutative Kazhdan-Lusztig cells

Richard M. Green[1]; Jozsef Losonczy[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)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 4, page 1025-1045
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Green, Richard M., and Losonczy, Jozsef. "Fully commutative Kazhdan-Lusztig cells." Annales de l’institut Fourier 51.4 (2001): 1025-1045. <http://eudml.org/doc/115932>.

@article{Green2001,
abstract = {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.},
affiliation = {Lancaster University, Department of Mathematics and Statistics, Lancaster LA1 4YF (Grande-Bretagne); Long Island University, Department of Mathematics, Brookville, NY 11548 (USA)},
author = {Green, Richard M., Losonczy, Jozsef},
journal = {Annales de l’institut Fourier},
keywords = {canonical basis; cell theory; Coxeter group; Hecke algebra; Kazhdan-Lusztig basis; Temperley-Lieb algebra; Hecke algebras; Coxeter groups; Kazhdan-Lusztig cells; fully commutative elements},
language = {eng},
number = {4},
pages = {1025-1045},
publisher = {Association des Annales de l'Institut Fourier},
title = {Fully commutative Kazhdan-Lusztig cells},
url = {http://eudml.org/doc/115932},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Green, Richard M.
AU - Losonczy, Jozsef
TI - Fully commutative Kazhdan-Lusztig cells
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 4
SP - 1025
EP - 1045
AB - 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.
LA - eng
KW - canonical basis; cell theory; Coxeter group; Hecke algebra; Kazhdan-Lusztig basis; Temperley-Lieb algebra; Hecke algebras; Coxeter groups; Kazhdan-Lusztig cells; fully commutative elements
UR - http://eudml.org/doc/115932
ER -

References

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  12. R.M. Green, J. Losonczy, A projection property for Kazhdan--Lusztig bases, Internat. Math. Res. Notices 1 (2000), 23-34 Zbl0961.20008MR1741607
  13. J.E. Humphreys, Reflection Groups and Coxeter Groups, (1990), Cambridge University Press, Cambridge Zbl0768.20016MR1066460
  14. D. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184 Zbl0499.20035MR560412
  15. J. Losonczy, The Kazhdan--Lusztig basis and the Temperley--Lieb quotient in type D, J. Algebra 233 (2000), 1-15 Zbl0969.20003MR1793587
  16. G. Lusztig, Cells in affine Weyl groups, II, J. Algebra 109 (1987), 536-548 Zbl0625.20032MR902967
  17. J.R. Stembridge, On the fully commutative elements of Coxeter groups, J. Algebraic Combin. 5 (1996), 353-385 Zbl0864.20025MR1406459

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