Real Subpairs and Frobenius-Schur Indicators of Characters in 2-Blocks
| dc.creator | Murray, John | |
| dc.date | 2008-11-10 | |
| dc.date.accessioned | 2026-07-07T10:17:15Z | |
| dc.date.available | 2026-07-07T10:17:15Z | |
| dc.description | Let B be a real 2-block of a finite group G. Then B has a real defect class. Let g be an element of such a class. A defect couple of B is (D,E), where E is a Sylow 2-subgroup of the extended centralizer C^*(g) of g, and D is the intersection of E with the centralizer C(g). It is known that (D,E) is uniquely determined up to G-conjugacy. We show that (D,E) determines which B-subpairs are real. We also outline how (D,E) influences the vertices of components of the G-permutation module corresponding to the conjugation action of G on its involutions. We apply these methods to enumerate the Frobenius-Schur indicators of the irreducible characters in a real block that has a dihedral defect group. We also determine the vertices of the components of the involution module in such a block. | |
| dc.description | 36 Pages | |
| dc.identifier | https://arxiv.org/abs/0811.1522 | |
| dc.identifier | http://arxiv.org/abs/0811.1522 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173791 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C20 | |
| dc.title | Real Subpairs and Frobenius-Schur Indicators of Characters in 2-Blocks | |
| dc.type | text |