By Susumi Ariki (auth.), Marc Cabanes (eds.)
Finite reductive teams and their representations lie on the middle of goup thought. After representations of finite normal linear teams have been decided through eco-friendly (1955), the topic used to be revolutionized by way of the creation of buildings from l-adic cohomology via Deligne-Lusztig (1976) and via the procedure of character-sheaves by way of Lusztig (1985). the speculation now additionally comprises the equipment of Brauer for the linear representations of finite teams in arbitrary attribute and the equipment of representations of algebras. It has develop into essentially the most energetic fields of latest mathematics.
The current quantity displays the richness of the paintings of specialists accrued at a global convention held in Luminy. Linear representations of finite reductive teams (Aubert, Curtis-Shoji, Lehrer, Shoji) and their modular elements Cabanes Enguehard, Geck-Hiss) cross aspect by means of facet with many comparable buildings: Hecke algebras linked to Coxeter teams (Ariki, Geck-Rouquier, Pfeiffer), advanced mirrored image teams (Broué-Michel, Malle), quantum teams and corridor algebras (Green), mathematics teams (Vignéras), Lie teams (Cohen-Tiep), symmetric teams (Bessenrodt-Olsson), and common finite teams (Puig). With the illuminating advent through Paul Fong, the current quantity kinds the simplest invitation to the field.
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Additional resources for Finite Reductive Groups: Related Structures and Representations: Proceedings of an International Conference held in Luminy, France
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H>. 7)). For odd primes p a result analogous to the Nakayama Conjecture holds for spin characters ([4], [2]); instead of removing Jrhooks you have to remove Jrbars. In this case a Jrblock cannot contain ordinary and spin characters at the same time. The weight of a block of spin characters is defined analogously to the weight of blocks of ordinary characters. In this paper we consider the case p = 2, where the characters of a 2-block B of Sn may be considered as the ordinary characters in a 53 Heights of Spin Characters unique 2-block B of Sn.
RG LU 0 RG L' . u'nu9. 12] pour un rappel de la definition) et ou Ie groupe G est a centre connexe (voir [S]). 2]), soit G est a centre connexe (voir [S]). • Deligne a demontre l'hypothese H3 (appelee formule de Mackey) dans Ie cas ou p et q sont suffisamment grands. 35 (1)]) . Forrnule des traces sur les corps finis 33 L'hypothese H3 implique que les applications Rr,u et *Rr,u, au niveau des fonctions centrales, sont independantes de U (voir par exemple [DM2, prop. 1]); nous les noterons dorenavant simplement et *Rr.
Fm)f- n Mo(n) mo(n) 1fi odd for i = 1, . ,l} {p r n 1 v2([p](l)) = O} = = IMo(n)1 For a partition a of n, we set s(a) = = s(lal), 2-core of a, and we write a E Mo as an abbreviation of a E Mo(lal). For a partition ,X = (ft, ... , fm) E V(n), we set a(2) 4-quotient of ,X (see [1, § 3]), ,X(4) a('x) = [n-2m]. 1 (Macdonald [6]) s lfn = L:2k ;, kI > k2 > . . +k • • i=I In fact, the set Mo(n) can be described explicitly using the 2-core tower (see [9, §6]). Using the notation of the theorem, a partition a belongs to Mo(n) if and only if there is exactly one 2-core (1) in the ki-th layer of the 2-core tower of a, for i = 1, ...
