Highest weight modules at the critical level and noncommutative Springer resolution
In the article by Bezrukavnikov and Mirkovic a certain non-commutative algebra A was defined starting from a semi-simple algebraic group, so that the derived category of A-modules is equivalent to the derived category of coherent sheaves on the Springer (or Grothendieck-Springer) resolution. Let gˇ...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
| Published: |
American Mathematical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/80850 https://orcid.org/0000-0001-5902-8989 |
| Summary: | In the article by Bezrukavnikov and Mirkovic a certain non-commutative algebra A was defined starting from a semi-simple algebraic group, so that the derived category of A-modules is equivalent to the derived category of coherent sheaves on the Springer (or Grothendieck-Springer) resolution.
Let gˇ be the Langlands dual Lie algebra and let [˄ over g] be the corresponding affine Lie algebra, i.e. [˄ over g] is a central extension of gˇ ⊗ C((t)).
Using results of Frenkel and Gaitsgory we show that the category of [˄ over g] modules at the critical level which are Iwahori integrable and have a fixed central character, is equivalent to the category of modules over a central reduction of A. This implies that numerics of Iwahori integrable modules at the critical level is governed by the canonical basis in the K-group of a Springer fiber, which was conjecturally described by Lusztig and constructed by Bezrukavnikov and Mirkovic. |
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