Timeline for extensions of IC sheaves
Current License: CC BY-SA 3.0
6 events
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| Jan 4, 2013 at 13:41 | comment | added | Dragos Fratila | I just realized that I haven't understood what a cuspidal local system is and that the above result about equivariant homology of the Steinberg variety might be covered in Lusztig's paper "Cuspidal ...I". I think I'm totally confused now about what these cuspidal local systems are... | |
| Jan 2, 2013 at 17:15 | comment | added | Dragos Fratila | @David: Thanks for the reference to Kato's paper. One more thing: I saw that in Chriss-Ginzburg they do the K-theoretic version but I couldn't find in their book the result that you mentioned (namely that the $G\times \mathbb{C}^*$-equivariant BM homology of the Steinberg variety is isomorphic to the degenerate affine Hecke algebra). Does it follow from the K-theoretic version? (putting q=1 gives only the group algebra of the affine Weyl group). | |
| Jan 2, 2013 at 1:05 | comment | added | David Ben-Zvi | @Dragos - No, sorry.. Lusztig's "cuspidal" papers are what I had in mind. You can look at papers of Syu Kato for more in this direction, but I don't know of anything more general. | |
| Jan 1, 2013 at 10:52 | comment | added | Dragos Fratila | @David. Thank you for the references. Actually I was hoping for a general method to say something about the dimensions of the BM homology of $Z\times_X Z$ where $Z\to X$ is a small map (or more generally semismall or just proper with $Z$ and $X$ smooth). This is, as you also said, a particular case of computing Ext groups between IC sheaves. Do you know of other examples of Ext algebras (or BM homology) computed explicitly? (apart from Varagnolo-Vasserot "KLR-algebras ... " and Lusztig's "cuspidal local systems") | |
| Dec 31, 2012 at 19:55 | history | edited | David Ben-Zvi | CC BY-SA 3.0 |
added 419 characters in body
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| Dec 31, 2012 at 18:09 | history | answered | David Ben-Zvi | CC BY-SA 3.0 |