Timeline for Kazhdan-Lusztig C-basis and categorification
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2012 at 15:19 | vote | accept | Thomas Gobet | ||
| Sep 26, 2012 at 15:41 | comment | added | Ben Webster♦ | The same way, just with slightly different conventions; you conjugate the projective story by $T_{w_0}$, since there is a derived equivalence sending projectives to tiltings lifting $T_{w_0}$. Alternatively, you get the basis of indecomposable projectives by applying indecomposable projective functors to the dominant Verma module (which is projective) and the indecomposable tiltings by applying them to the anti-dominant Verma module (which is tilting). | |
| Sep 26, 2012 at 9:16 | comment | added | Thomas Gobet | Thank you for this answer. In case we match the $C'$-basis with projective modules of a graded version of category $\mathcal{O}$ then the Hecke algebra is categorified as a module over itself by graded translation functors which categorify the right multiplication by elements of the $C'$-basis. In case I follow your idea is it obvious on how to categorifiy the Hecke algebra as a module over itself ? | |
| Sep 26, 2012 at 1:17 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
added 28 characters in body
|
| Sep 26, 2012 at 0:52 | history | answered | Ben Webster♦ | CC BY-SA 3.0 |