Timeline for Representations of finite Coxeter groups
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Jan 31, 2011 at 10:22 | comment | added | Sheikraisinrollbank | @Victor: I don't understand why the iso. between CW and the Hecke algebra at non-zero q that isn't a root of unity should be canonical at all (though I believe that specific iso's have been written down). In fact it seems reasonable that there should be one such iso. for each homotopy class of paths from 1 to q (in the space of q for which the Hecke algebra is semisimple). | |
| Jul 21, 2010 at 7:03 | vote | accept | Pooja Singla | ||
| Jul 16, 2010 at 13:16 | comment | added | Pooja Singla | Oh ok I am really sorry then for wrong use of word 'generic'. Yeah as a first case I want to know about representations of C[W] for any coxeter group W. Would you please comment on that? I shall be greatly thankful for that. My apologies for my little knowledge in this area. | |
| Jul 16, 2010 at 4:38 | comment | added | Victor Protsak | For $q=1$ the Hecke algebra by definition coincides with the group algebra of the corresponding Coxeter group $\mathbb{C}[W]$, so it is in no way "generic" case. For non-zero $q$ that isn't the root of unity, the algebra is semisimple and canonically isomorphic to $\mathbb{C}[W].$ Therefore, multiplicity=dimension is the same as for $W$. Is that what you were looking for? NB: "Generic" implies that $q$ is treated as a parameter and the Hecke algebra is considered over the ring $\mathbb{C}[q,q^{-1}]$ or its extension. | |
| Jul 14, 2010 at 17:09 | history | edited | Pooja Singla | CC BY-SA 2.5 |
added 282 characters in body
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| Jul 14, 2010 at 16:57 | comment | added | Victor Protsak | Please, clarify what kind of information you need and what you mean by "their multiplicities". | |
| Jul 14, 2010 at 16:52 | answer | added | Victor Protsak | timeline score: 6 | |
| Jul 14, 2010 at 16:38 | answer | added | Jim Humphreys | timeline score: 10 | |
| Jul 14, 2010 at 16:16 | history | edited | Charles Matthews | CC BY-SA 2.5 |
upper case
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| Jul 14, 2010 at 15:44 | history | asked | Pooja Singla | CC BY-SA 2.5 |