Timeline for Kazhdan-Lusztig C-basis and categorification
Current License: CC BY-SA 3.0
12 events
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| Sep 28, 2012 at 15:19 | vote | accept | Thomas Gobet | ||
| Sep 26, 2012 at 0:52 | answer | added | Ben Webster♦ | timeline score: 5 | |
| Sep 25, 2012 at 16:11 | comment | added | David Hill | I should add that even if the lattices are the same, one can still make sense of all this. For example, the C basis may correspond to simple objects and the C' basis corresponds to so-called standard objects. | |
| Sep 25, 2012 at 15:58 | comment | added | David Hill | How are the $\mathbb{Z}[q,q^{-1}]$-lattices spanned by the C and C' bases related? Often in categorification one sees two lattices. One lattice is spanned by projective objects while the other is spanned by simples. The minus signs in the change of basis can interpreted as taking the Euler characteristic of a projective resolution. | |
| Sep 25, 2012 at 10:02 | history | edited | Thomas Gobet | CC BY-SA 3.0 |
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| Sep 25, 2012 at 9:56 | history | edited | Thomas Gobet | CC BY-SA 3.0 |
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| Sep 25, 2012 at 9:51 | history | edited | Thomas Gobet | CC BY-SA 3.0 |
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| Sep 25, 2012 at 9:45 | history | edited | Thomas Gobet | CC BY-SA 3.0 |
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| Sep 24, 2012 at 17:56 | comment | added | Alexander Woo | The remark at the end of Section 7.9 in Humphreys connects the C and C' bases by an automorphism of the Hecke algebra. If your elements don't already depend on the specifics of your categorification, you might be better off pushing your elements through that automorphism and studying their images. | |
| Sep 24, 2012 at 15:02 | comment | added | David Ben-Zvi | Could you remind us which are the C and C' bases? When I hear "Kazhdan-Lusztig basis" I think (or rather I repeat what what K-L themselves said) intersection cohomology sheaves on the flag variety, which is already a natural categorified interpretation, but maybe you mean some variant? | |
| Sep 24, 2012 at 11:58 | history | edited | Thomas Gobet | CC BY-SA 3.0 |
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| Sep 24, 2012 at 11:35 | history | asked | Thomas Gobet | CC BY-SA 3.0 |