On the generic degrees of cyclotomic algebras

Malle, Gunter

doi:10.1090/S1088-4165-00-00088-1

On the generic degrees of cyclotomic algebras
HTML articles powered by AMS MathViewer

by Gunter Malle PDF

Represent. Theory 4 (2000), 342-369 Request permission

Abstract:

We determine the generic degrees of cyclotomic Hecke algebras attached to exceptional finite complex reflection groups. The results are used to introduce the notion of spetsial reflection group, which in a certain sense is a generalization of the finite Weyl group. In particular, to spetsial $W$ there is attached a set of unipotent degrees which in the case of a Weyl group is just the set of degrees of unipotent characters of finite reductive groups with Weyl group $W$, and in general enjoys many of their combinatorial properties.

References

Rudolph E. Langer, The boundary problem of an ordinary linear differential system in the complex domain, Trans. Amer. Math. Soc. 46 (1939), 151–190 and Correction, 467 (1939). MR 84, DOI 10.1090/S0002-9947-1939-0000084-7
Stefan Kempisty, Sur les fonctions à variation bornée au sens de Tonelli, Bull. Sém. Math. Univ. Wilno 2 (1939), 13–21 (French). MR 46
Michel Broué and Gunter Malle, Zyklotomische Heckealgebren, Astérisque 212 (1993), 119–189 (German). Représentations unipotentes génériques et blocs des groupes réductifs finis. MR 1235834

Towards spetses II

Michel Broué, Gunter Malle, and Raphaël Rouquier, Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998), 127–190. MR 1637497, DOI 10.1515/crll.1998.064
Michel Broué and Jean Michel, Sur certains éléments réguliers des groupes de Weyl et les variétés de Deligne-Lusztig associées, Finite reductive groups (Luminy, 1994) Progr. Math., vol. 141, Birkhäuser Boston, Boston, MA, 1997, pp. 73–139 (French). MR 1429870, DOI 10.1007/978-1-4612-4124-9_{4}

Weights of Markov traces and generic degrees

Characters of finite Coxeter groups and Iwahori-Hecke algebras

I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), 590–622. MR 81, DOI 10.1215/S0012-7094-39-00549-1
George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472, DOI 10.1515/9781400881772
George Lusztig, Appendix: Coxeter groups and unipotent representations, Astérisque 212 (1993), 191–203. Représentations unipotentes génériques et blocs des groupes réductifs finis. MR 1235835
J. C. Oxtoby and S. M. Ulam, On the existence of a measure invariant under a transformation, Ann. of Math. (2) 40 (1939), 560–566. MR 97, DOI 10.2307/1968940
Gunter Malle, Degrés relatifs des algèbres cyclotomiques associées aux groupes de réflexions complexes de dimension deux, Finite reductive groups (Luminy, 1994) Progr. Math., vol. 141, Birkhäuser Boston, Boston, MA, 1997, pp. 311–332 (French). MR 1429878, DOI 10.1007/978-1-4612-4124-9_{1}2
Gunter Malle, Spetses, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, pp. 87–96. MR 1648059

On the rationality and fake degrees of characters of cyclotomic algebras

6

Giovanni Cutolo, John C. Lennox, Silvana Rinauro, Howard Smith, and James Wiegold, On infinite core-finite groups, Proc. Roy. Irish Acad. Sect. A 96 (1996), no. 2, 169–175. MR 1641198, DOI 10.1515/crll.1982.336.201