Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras

In this thesis, we examine three different versions of "categorification" of the affine Hecke algebra and its periodic module: the first is by equivariant coherent sheaves on the Grothendieck resolution (and related objects), the second is by certain classes on bimodules over polynomial rings, called Soergel bimodules, and the third is by certain categories of constructible sheaves on the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the categories involved; which strengthens a theorem of Bezrukavnikov-Riche.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2011

Author dc:creator

• Dodd, Christopher Stephen

Advisor dc:contributor.advisor

• Roman Bezrukavnikov.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/67788

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/67788