Timeline for What is the effect of tensoring with the sign representation on irreducible modules for a Type D Weyl group?
Current License: CC BY-SA 4.0
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| Dec 29, 2023 at 14:01 | comment | added | Jay Taylor | That is an error in the book of Geck & Pfeiffer that comes from some subtle labelling issues. For the correction see Lemma 3.5 in the paper "On Kottwitz' conjecture for twisted involutions" by Geck arxiv.org/abs/1206.0443 | |
| Dec 20, 2023 at 2:34 | comment | added | Christopher Drupieski | Yes, Remark 5.6.5 in the book by Geck and Pfeiffer seems to directly address my original question, although the way I'm reading the statement, it seems to imply that $V^{(\lambda,\lambda)^+} \otimes sgn \cong V^{(\lambda,\lambda)^+}$ for all $n$, not just for $n$ even as stated by @KentaSuzuki. I'm not sure at this point if I'm misreading something. | |
| Dec 19, 2023 at 17:03 | comment | added | Joshua Mundinger | @ChristopherDrupieski You may also find the following text useful: Characters of Finite Coxeter groups and Iwahori-Hecke algebras by Geck and Pfeiffer. | |
| Dec 19, 2023 at 14:17 | comment | added | Christopher Drupieski | Now that I understand what I'm looking at a bit better, I think perhaps the construction in the answer is detailed in Section 3 of the paper "On the characters of the Weyl group of type D" by S.J. Mayer (Math. Proc. Camb. Phil. Soc. (1975), 77, 259). | |
| Dec 19, 2023 at 0:12 | vote | accept | Christopher Drupieski | ||
| Dec 18, 2023 at 15:07 | comment | added | Christopher Drupieski | Thanks for this. Do you have a favorite reference one could cite for these details (or is this instead a matter of unwinding more general results in the context of $W(D_{2n})$)? | |
| Dec 18, 2023 at 11:54 | history | edited | Kenta Suzuki | CC BY-SA 4.0 |
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| Dec 18, 2023 at 2:21 | history | answered | Kenta Suzuki | CC BY-SA 4.0 |