Open AccessTwisting functors on 𝒪
Author(s) -
Henning Haahr Andersen,
Catharina Stroppel
Publication year - 2003
Publication title -
representation theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.169
H-Index - 37
ISSN - 1088-4165
DOI - 10.1090/s1088-4165-03-00189-4
Subject(s) - functor , mathematics , equivalence (formal languages) , class (philosophy) , block (permutation group theory) , annotation , semantics (computer science) , pure mathematics , algebra over a field , computer science , combinatorics , artificial intelligence , programming language
This paper studies twisting functors on the main block of the Bernstein-Gelfand-Gelfand category O \mathcal {O} and describes what happens to (dual) Verma modules. We consider properties of the right adjoint functors and show that they induce an auto-equivalence of derived categories. This allows us to give a very precise description of twisted simple objects. We explain how these results give a reformulation of the Kazhdan-Lusztig conjectures in terms of twisting functors.