zbMATH — the first resource for mathematics

Special involutions and bulky parabolic subgroups in finite Coxeter groups. (English) Zbl 1078.20042
Summary: The conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short intrinsic characterisation of special involutions in terms of so-called bulky parabolic subgroups.

20F55 Reflection and Coxeter groups (group-theoretic aspects)
06A07 Combinatorics of partially ordered sets
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
Full Text: DOI
[1] DOI: 10.1007/BF02568285 · Zbl 0790.52006 · doi:10.1007/BF02568285
[2] Felder, J. Eur. Math. Soc. (JEMS) 7 pp 101– (2005)
[3] DOI: 10.1007/s002220050312 · Zbl 0926.20024 · doi:10.1007/s002220050312
[4] Bourbaki, Groupes et algèbres de Lie. Chapitres IV–VI (1968) · Zbl 0186.33001
[5] DOI: 10.1080/00927878208822739 · Zbl 0531.20016 · doi:10.1080/00927878208822739
[6] DOI: 10.1016/0097-3165(93)90060-L · Zbl 0838.20045 · doi:10.1016/0097-3165(93)90060-L
[7] Richardson, Bull. Austral. Math. Soc. 26 pp 1– (1982)
[8] Lehrer, The Arcata Conference on Representations of Finite Groups (Arcata, CA, 1986) pp 219– (1987) · doi:10.1090/pspum/047.2/933414
[9] DOI: 10.1112/jlms/s2-21.1.62 · Zbl 0427.20040 · doi:10.1112/jlms/s2-21.1.62
[10] Geck, Characters offinite Coxeter groups and Iwahori-Hecke algebras (2000) · Zbl 0996.20004
[11] DOI: 10.1112/jlms/s2-36.2.275 · Zbl 0649.20041 · doi:10.1112/jlms/s2-36.2.275
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.