Timeline for $q$-(and other)-analogs for counting index-$n$ subgroups in terms of Homs to $S_n$?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2017 at 17:36 | vote | accept | Alexander Chervov | ||
| Jun 14, 2017 at 17:02 | comment | added | Alexander Chervov | Quantum linear groups an representations of GLn(Fq) J Brundan, R Dipper, AS Kleshchëv - 2001 - books.google.com google.ru/… | |
| Jun 14, 2017 at 17:01 | comment | added | Alexander Chervov | @TimothyChow Well ... Hecke algebra is part of GL(n,F_q) - I mean consider group algebra and its part bi-invariant (left and right) for Borel subalgebra - that will be precisely Hecke algebra. (By Brua decopmposition GL = BorelS_nBorel -- so facrotring out Borel - the size will be like S_n, but the product will be deformed). In that way Hecke algebra appeared much earlier than "quantum groups". And its miracle that the same algebra appeared in Schur-Weyl duality for U_q(gl). On the other hand recent papers relate U_q(gl) and GL(n,F_q) see: | |
| Jun 14, 2017 at 13:31 | comment | added | Timothy Chow | "$q$-analogues of $S_n$" makes me think "Hecke algebra," though I'm not sure that makes that much sense here... | |
| Jun 12, 2017 at 22:43 | answer | added | Ofir Gorodetsky | timeline score: 15 | |
| Jun 12, 2017 at 21:32 | history | edited | YCor | CC BY-SA 3.0 |
corrected typos and typing; added co tag.
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| Jun 12, 2017 at 20:10 | comment | added | Douglas Zare | One way I think about that formula is that $G$ acts transitively on the $n$ cosets of a subgroup of index $n$, and permutation representations can be built from transitive permutation representations. | |
| Jun 12, 2017 at 19:41 | history | edited | Alexander Chervov | CC BY-SA 3.0 |
added 108 characters in body
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| Jun 12, 2017 at 19:23 | history | asked | Alexander Chervov | CC BY-SA 3.0 |