Geometric braid group action on derived categories of coherent sheavesReport as inadecuate




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1 LMBP - Laboratoire de Mathématiques Blaise Pascal

Abstract : In this paper we give, for semi-simple groups without factors of type G 2, a geometric construction of a braid group action on the derived category of coherent sheaves on the Grothendieck resolution extending the action constructed by Bezrukavnikov, Mirkovic and Rumynin. It follows that this action extends to characteristic zero, where it also has some nice representation-theoretic interpretations. The argument uses a presentation of the affine braid group analogous to the ``Bernstein presentation- of the corresponding Hecke algebra this presentation was suggested by Lusztig; it is worked out in the appendix, joint with Roman Bezrukavnikov.





Author: Simon Riche -

Source: https://hal.archives-ouvertes.fr/



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