On Arkhipov’s and Enright’s functors

Springer Science and Business Media LLC - 2004
Oleksandr Khomenko1, Volodymyr Mazorchuk2
1Mathematisches Institut der Universität Freiburg, Freiburg im Breisgau, Germany
2Department of Mathematics, Uppsala University, Uppsala, Sweden

Tóm tắt

We give a description of Arkhipov’s and (Joseph’s and Deodhar-Mathieu’s versions of) Enright’s endofunctors on the category 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.

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