2011年1月13日
On localization of the rational Cherednik algebras and other algebras
Introduction to Cherednik algebras
- 記述言語
- 英語
- 会議種別
- 口頭発表(一般)
- 主催者
- Graduate School of Mathematics, Nagoya Univ.
- 開催地
- Graduate School of Mathematics, Nagoya Univ.
In this talk, I will survey the new scheme for localization of some noncommutative algebras which is first established by Kashiwara and Rouquier. Both the rational Cherednik algebras and the finite W-algebras are algebras constructed as quantization of some symplectic singularities. To consider localization of these algebras, the main problem is that, although we have symplectic resolutions of these symplectic singularities, these resolutions are never isomorphic to cotangent bundles of complex manifolds. To solve the above problem, Kashiwara-Rouquier made use of the theory of the Deformation-Quantization algebras for localization of the rational Cherednik algebra with respect to the symmetric group. After Kashiwara-Rouqier, similar constructions of localization were obtained for the finite W-algebras by Dodd-Kremnizter, and for noncommutative deformations of hypertoric varieties by Bellamy-Kuwabara.