zbMATH — the first resource for mathematics

Minimal length elements in twisted conjugacy classes of finite Coxeter groups. (English) Zbl 1042.20026
Summary: Let \(W\) be a finite Coxeter group and let \(F\) be an automorphism of \(W\) that leaves the set of generators of \(W\) invariant. We establish certain properties of elements of minimal length in the \(F\)-conjugacy classes of \(W\) that allow us to define character tables for the corresponding twisted Iwahori-Hecke algebras. These results are extensions of results obtained by Geck and Pfeiffer in the case where \(F\) is trivial.

20F55 Reflection and Coxeter groups (group-theoretic aspects)
20E45 Conjugacy classes for groups
20C08 Hecke algebras and their representations
Full Text: DOI
[1] Broué, M.; Michel, J., Sur certains éléments réguliers des groupes de Weyl et LES variétés de deligne – lusztig associées, (), 73-139 · Zbl 1029.20500
[2] Brieskorn, E.; Saito, K., Artin-gruppen and Coxeter-gruppen, Invent. math., 17, 245-271, (1972) · Zbl 0243.20037
[3] Carter, R.W., Conjugacy classes in the Weyl group, Compositio math., 25, 1-59, (1972) · Zbl 0254.17005
[4] Carter, R.W., Finite groups of Lie type: conjugacy classes and complex characters, (1985), Wiley New York · Zbl 0567.20023
[5] Char, B.W., Maple V, language reference manual, (1991), Springer-Verlag Berlin/New York
[6] C. W. Curtis, and, I. Reiner, Methods of Representation Theory, Vols, 1, and, 2, Wiley, New York, 1981, and, 1987. · Zbl 0469.20001
[7] Deligne, P., LES immeubles des groupes de tresses généralisés, Invent. math., 17, 273-302, (1972) · Zbl 0238.20034
[8] Digne, F.; Michel, J., Fonctions \(L\) des variétés de deligne – lusztig et descente de shintani, Mém. soc. math. France, 20, (1985) · Zbl 0608.20027
[9] Geck, M.; Pfeiffer, G., On the irreducible characters of Hecke algebras, Adv. math., 102, 79-94, (1993) · Zbl 0816.20034
[10] Geck, M.; Hiss, G.; Lubeck, F.; Malle, G.; Pfeiffer, G., CHEVIE—A system for computing and processing generic character tables, Appl. algebra engrg. comm. comput., 7, 175-210, (1996) · Zbl 0847.20006
[11] Geck, M.; Michel, J., “good” elements of finite Coxeter groups and representations of iwahori – hecke algebras, Proc. London math. soc., 74, 275-305, (1997) · Zbl 0877.20027
[12] Halverson, T.; Ram, A., Murnaghan – nakayama rules for characters of iwahori – hecke algebras of classical type, Trans. amer. math. soc., 348, 3967-3995, (1996) · Zbl 0876.20009
[13] Humphreys, J.E., Reflection groups and Coxeter groups, Cambridge studies in advanced mathematics, 29, (1990), Cambridge Univ. Press Cambridge
[14] Kim, S., Mots de longueur maximale dans une classe de conjugaison d’un groupe symétrique, vu comme groupe de Coxeter, C. R. acad. sci. Paris Sér. I math., 327, 617-622, (1998) · Zbl 0981.20001
[15] Lusztig, G., Characters of reductive groups over a finite field, Annals of mathematics studies, 107, (1984), Princeton Univ. Press Princeton · Zbl 0556.20033
[16] Schönert, M., GAP—groups, algorithms, and programming, (1994), Lehrstuhl D für Mathematik Aachen
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.