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Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic
- Source :
- Nagoya Math. J. 184 (2006), 1-55
- Publication Year :
- 2006
- Publisher :
- Cambridge University Press (CUP), 2006.
-
Abstract
- In math.RT/0205144 we observed that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character can be identified with coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber. In the present paper we treat singular central characters. The basic step is the Beilinson-Bernstein localization of modules with a fixed (generalized) central character as sheaves on the partial flag variety corresponding to the singularity of the character. These sheaves are modules over a sheaf of algebras which is a version of twisted crystalline differential operators, but is actually larger. We discuss translation functors and intertwining functors. The latter generate an action of the affine braid group on the derived category of modules with a regular (generalized) central character, which intertwines different localization functors. We also describe the standard duality on Lie algebra modules in terms of D-modules and coherent sheaves.<br />some minor corrections and expansions
- Subjects :
- Pure mathematics
Derived functor
General Mathematics
(g,K)-module
18F99
01 natural sciences
Representation theory
Coherent sheaf
Mathematics - Algebraic Geometry
Mathematics::Category Theory
0103 physical sciences
FOS: Mathematics
Representation Theory (math.RT)
0101 mathematics
Mathematics::Representation Theory
Algebraic Geometry (math.AG)
Mathematics
Discrete mathematics
Derived category
010308 nuclear & particles physics
Computer Science::Information Retrieval
010102 general mathematics
16. Peace & justice
Affine Lie algebra
16E20
17B50
Ext functor
Sheaf
Mathematics - Representation Theory
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 183
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....f7737d2b08f837a539644b18889d88ab