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Mathematische Zeitschrift

, Volume 249, Issue 2, pp 357–386 | Cite as

On Arkhipov’s and Enright’s functors

  • Oleksandr Khomenko
  • Volodymyr Mazorchuk
Article

Abstract.

We give a description of Arkhipov’s and (Joseph’s and Deodhar-Mathieu’s versions of) Enright’s endofunctors on the category Open image in new window associated with a fixed triangular decomposition of a complex finite-dimensional semi-simple Lie algebra, in terms of (co)approximation functors with respect to suitably chosen injective (resp. projective) modules. We establish some new connections between these functors, for example we show that Arkhipov’s and Joseph’s functors are adjoint to each other. We also give several proofs of braid relations for Arkhipov’s and Enright’s functors.

Keywords

Approximation Functor Triangular Decomposition Braid Relation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität FreiburgFreiburg im BreisgauGermany
  2. 2.Department of MathematicsUppsala UniversityUppsalaSweden

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