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Affine braid group actions on derived categories of Springer resolutions

Roman Bezrukavnikov, Simon Riche (2012)

Annales scientifiques de l'École Normale Supérieure

In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...

Alcôves et p -rang des variétés abéliennes

Bao Chau Ngô, Alain Genestier (2002)

Annales de l’institut Fourier

On étudie la relation entre le p -rang des variétés abéliennes en caractéristique p et la stratification de Kottwitz-Rapoport de la fibre spéciale en p de l’espace de module des variétés abéliennes principalement polarisées avec structure de niveau de type Iwahori en p . En particulier, on démontre la densité du lieu ordinaire dans cette fibre spéciale.

Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 )

Yu Wang, Xiaoming Li (2023)

Czechoslovak Mathematical Journal

Let U be the two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 ) and F ( U ) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F ( U ) in the case when r s - 1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.

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