On functors associated to a simple root

Mazorchuk, V. and Stroppel, C. (2007) On functors associated to a simple root. Journal of Algebra, 314(1), pp. 97-128. (doi: 10.1016/j.jalgebra.2007.03.015)

Abstract

Associated to a simple root of a finite-dimensional complex semisimple Lie algebra, there are several endofunctors (defined by Arkhipov, Enright, Frenkel, Irving, Jantzen, Joseph, Mathieu, Vogan and Zuckerman) on the BGG category O. We study their relations, compute cohomologies of their derived functors and describe the monoid generated by Arkhipov's and Joseph's functors and the monoid generated by Irving's functors. It turns out that the endomorphism rings of all elements in these monoids are isomorphic. We prove that the functors give rise to an action of the singular braid monoid on the bounded derived category of O_o. We also use Arkhipov's, Joseph's and Irving's functors to produce new generalized tilting modules.

• Item Type: Articles
• Keywords: Lie algebra, category O, functor, translation, twisting, module
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mazorchuk, Dr Volodymyr and Stroppel, Dr Catharina
• Authors: Mazorchuk, V., and Stroppel, C.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Algebra
• Journal Abbr.: J. algebra
• Publisher: Elsevier
• ISSN: 0021-8693
• ISSN (Online): 1090-266X
• Published Online: 23 March 2007
• Copyright Holders: Copyright © 2007 Elsevier
• First Published: First published in Journal of Algebra 314(1):97-128
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher