A note on Hecke patterns in Category O

We study the family of derived auto-equivalences of the BGG-category O that correspond to the action of the standard generators of the Hecke algebra. Both the non-graded and graded situations are considered.Comment: 20 pages, some typos in previous version fixed, proof of Thm. 9.6 expanded, acknowledgments added, all comments welcom

Derived equivalences and sl_2-categorifications for U_q(gl_n)

We give a construction of sl_2-categorifications (in the sense of Chuang-Rouquier) for representations of U_q(gl_n), for generic q and for q a root of unity.Comment: 15 pages, references added, exposition streamlined, all comments welcom

A remark on some bases in the Hecke algebra

We consider some bases in the Hecke algebra and exhibit certain dualities between them.Comment: 6 pages, exposition streamlined, all comments welcom