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$C^{*}$ algebras associated with von Neumann algebras

Tullio G. Ceccherini-Silberstein (1999)

Bollettino dell'Unione Matematica Italiana

Ad un'algebra di von Neumann separabile $M$ , in forma standard su di uno spazio di Hilbert $H$ , si associa la $C^{*}$ algebra $O_{M}$ definita come la $C^{*}$ algebra $O_{U (M)}$ costituita dai punti fissi dell'algebra di Cuntz generalizzata $O_{H}$ mediante l'azione canonica del gruppo $U (M)$ degli unitari di $M$ . Si dà una caratterizzazione di $O_{M}$ nel caso in cui $M$ è un fattore iniettivo. In seguito, come applicazione della teoria dei sistemi asintoticamente abeliani, si mostra che, se $ω$ è uno stato vettoriale normale e fedele di $M$ , la restrizione...

Caractères d'algèbres de Lie finies

Tonny A. Springer (1974/1975)

Séminaire Dubreil. Algèbre et théorie des nombres

Caractères de groupes de Chevalley finis

T. A. Springer (1972/1973)

Séminaire Bourbaki

Caractères des groupes réductifs finis et $𝒟$ -modules

Michel Gros (2001)

Rendiconti del Seminario Matematico della Università di Padova

Caractères unipotents de 3D4(Fq).

N. Spaltenstein (1982)

Commentarii mathematici Helvetici

Catégories dérivées et variétés de Deligne-Lusztig

Cédric Bonnafé, Raphaël Rouquier (2003)

Publications Mathématiques de l'IHÉS

Catégories tannakiennes

Neantro Saavedra Rivano (1972)

Bulletin de la Société Mathématique de France

Category $𝒪$ for quantum groups

Henning Haahr Andersen, Volodymyr Mazorchuk (2015)

Journal of the European Mathematical Society

In this paper we study the BGG-categories $𝒪_{q}$ associated to quantum groups. We prove that many properties of the ordinary BGG-category $𝒪$ for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when $q$ is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for $𝒪$ and for finite dimensional $U_{q}$ -modules we are able to determine...

Cellular algebras.

G.I. Lehrer, J.J. Graham (1996)

Inventiones mathematicae

Certain unipotent representations of finite Chevalley groups and Picard–Lefschetz monodromy

Akihiko Gyoja (2002)

Annales scientifiques de l'École Normale Supérieure

Character formulae for classical groups

Péter Frenkel (2006)

Open Mathematics

We give formulae relating the value Xλ (g) of an irreducible character of a classical group G to entries of powers of the matrix g ε G. This yields a far-reaching generalization of a result of J.L. Cisneros-Molina concerning the GL 2 case [1].

Chern classes of reductive groups and an adjunction formula

Valentina Kiritchenko (2006)

Annales de l’institut Fourier

In this paper, I construct noncompact analogs of the Chern classes for equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the (topological) Euler characteristic of complete intersections in reductive groups. In the case where a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. I also prove that the higher Chern classes vanish. The first...

Classification of spherical varieties

Paolo Bravi (2010)

Les cours du CIRM

We give a short introduction to the problem of classification of spherical varieties, by presenting the Luna conjecture about the classification of wonderful varieties and illustrating some of the related currently known results.

Classification of strict wonderful varieties

Paolo Bravi, Stéphanie Cupit-Foutou (2010)

Annales de l’institut Fourier

In the setting of strict wonderful varieties we prove Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that primitive strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits and model spaces. To make the paper as self-contained as possible, we also gather some known results on these families and more generally on wonderful varieties.

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