Timeline for Morita equivalence between category of modules of hyperoctahedral group with the category of modules of direct product of two symmetric groups
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 24 at 14:30 | comment | added | noone | The Specht module of $W_n$ is spanned by all polytabloids [Theorem 2.18, numdam.org/item/?id=AST_1981__87-88__267_0]. In the above-mentioned paper, the Specht module is defined by $z_{\lambda} W_n$. Could you please help me to understand the connection between them. | |
| Sep 15 at 22:03 | comment | added | Andrew | It is easier to go in the reverse direction: a Specht module $π^πβπ^π$ for $π_π\times π_{πβ1}$ is sent to the Specht module $π^{(π,π)}$ for $W_π$. More generally, $π\otimes π$ is sent to $\operatorname{Ind}^{W_π}_{π_π×π_{πβπ}}(π\otimes π)$. See Prop. 4.11 of Dipper-Mathas "Morita equivalences of ArikiβKoike algebras", Math. Z, 240 (2002), 579-610. The inverse equivalence should be given by suitable restriction functors. | |
| Sep 13 at 14:02 | comment | added | LSpice | You used both $d$ and $n$, as far as I could tell with the same meaning. I changed $d$ to $n$. I hope that that was all right. | |
| Sep 13 at 14:02 | history | edited | LSpice | CC BY-SA 4.0 |
Link syntax; $d$ -> $n$
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| Sep 13 at 13:29 | history | asked | noone | CC BY-SA 4.0 |