On the “Bruhat graph” of a Coxeter system

Matthew Dyer

Compositio Mathematica (1991)

  • Volume: 78, Issue: 2, page 185-191
  • ISSN: 0010-437X

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Dyer, Matthew. "On the “Bruhat graph” of a Coxeter system." Compositio Mathematica 78.2 (1991): 185-191. <http://eudml.org/doc/90085>.

@article{Dyer1991,
author = {Dyer, Matthew},
journal = {Compositio Mathematica},
keywords = {Bruhat graph; finite Coxeter system; Bruhat order; reflection subgroups; posets of fixed length; Kazhdan-Lusztig polynomial},
language = {eng},
number = {2},
pages = {185-191},
publisher = {Kluwer Academic Publishers},
title = {On the “Bruhat graph” of a Coxeter system},
url = {http://eudml.org/doc/90085},
volume = {78},
year = {1991},
}

TY - JOUR
AU - Dyer, Matthew
TI - On the “Bruhat graph” of a Coxeter system
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 78
IS - 2
SP - 185
EP - 191
LA - eng
KW - Bruhat graph; finite Coxeter system; Bruhat order; reflection subgroups; posets of fixed length; Kazhdan-Lusztig polynomial
UR - http://eudml.org/doc/90085
ER -

References

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  1. [BGG] Bernstein, I.N., Gelfand, I.M. and Gelfand, S.I., Structure of representations generated by highest weight vectors (English translation)Funct. Anal. Appl.5 (1971) 1-8. Zbl0246.17008
  2. [B] Bjorner, A., Orderings of Coxeter groups, in " Combinatorics and algebra (Boulder, Colo.1983)", Contemp Math34, Amer. Math. Soc., Providence, R. I (1984). Zbl0594.20029MR777701
  3. [BW] Bjorner, A. and Wachs, M., Bruhat order of Coxeter groups and shellability, Adv. in Math.43 (1982), 87-100. Zbl0481.06002MR644668
  4. [C] Carter, R.W., Finite groups of Lie type, John Wiley & Sons, Chichester (1985). Zbl0567.20023MR794307
  5. [D] Davis, M.W., Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math.117(2) (1983) 293-324. Zbl0531.57041MR690848
  6. [De] Deodhar, V., On the root system of a Coxeter group, Comm. Alg.10 (1982) 611-630. Zbl0491.20032MR647210
  7. [Dy1] Dyer, M., Hecke algebras and reflections in Coxeter groups, Ph.D. Thesis, University of Sydney (1987). 
  8. [Dy2] Dyer, M., Reflection subgroups of Coxeter systems, to appear in J. of Alg. Zbl0712.20026MR1076077
  9. [Dy3] Dyer, M., Hecke algebras and shellings of Bruhat intervals, preprint. Zbl0817.20045
  10. [Dy4] Dyer, M., Hecke algebras and shellings of Bruhat intervals II; twisted Bruhat orders, preprint. Zbl0817.20045MR1197833
  11. [J] Jantzen, J.C., Representations of algebraic groups, Pure and Applied Math. Vol. 131, Academic Press, Boston (1987). Zbl0654.20039MR899071
  12. [KL] Kazhdan, D. and Lusztig, G., Representations of Coxeter groups and Hecke algebras, Invent. Math.53 (1979), 165-184. Zbl0499.20035MR560412

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