Bases for the Bruhat-Chevalley order on all finite Coxeter groups

Journal of Algebra

Volumn 197, Issue 1, 1997, Pages 278-310

  Geck, Meinolf ^a   Kim, Sungsoon ^a,b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b Yonsei University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031281954     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1997.7096     Document Type: Article

References (10)

1. 1. N. Bourbaki, "Groupes et algèbres de Lie," Chaps. IV-VI, Hermann, Paris, 1968.
2. 2. V. V. Deodhar, Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math. 39 (1977), 187-198.
3. 3. M. Dyer, "Hecke Algebras and Reflections in Coxeter Groups," Ph.D. thesis, University of Sydney, 1987.
4. 4. C. Ehresmann, Sur la topologie de certains espaces homogènes, Ann. of Math. 35 (1934), 396-443.
5. 5. M. Geck, G. Hiss, F. Lübeck, G. Malle, and G. Pfeiffer, CHEVIE-A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras, Appl. Algebra Engrg. Comm. Comput. 7 (1996), 175-210.
6. 6. J. E. Humphreys, "Reflection Groups and Coxeter Groups," Cambridge Stud. Adv. Math., Vol. 29, Cambridge Univ. Press, Cambridge, 1990.
7. 7. A. Lascoux and M. P. Schützenberger, Treillis et bases des groupes de Coxeter, Electron. J. Combin. 3 (1995).
8. 8. G. Lusztig, "Characters of Reductive Groups over a Finite Field," Ann. Math. Studies, Vol. 107, Princeton Univ. Press, Princeton, NJ, 1984.
9. 9. R. A. Proctor, Classical Bruhat orders and lexicographic shellability, J. Algebra 77 (1982), 104-126.
10. 10. M. Schönert et al., "GAP - Groups, Algorithms, and Programming," Lehrstuhl D für Mathematik, fourth ed., RWTH Aachen, Germany, 1994.