Real subpairs and Frobenius-Schur indicators of characters in 2-blocks

JOURNAL OF ALGEBRA

卷:322

Article

Murray, John

关键词: Block;    Dihedral defect group;    Frobenius-Schur indicator;    Extended defect group;    Subpairs;   

DOI  :  10.1016/j.jalgebra.2009.04.016

来源: Elsevier

【 摘 要 】

Let B be a real 2-block of a finite group S. A defect couple of B is a certain pair (D, E) of 2-subgroups of G, such that D is a defect group of B, and D <= E. The block B is principal if E = D; otherwise [E : D] = 2. We show that (D, E) determines which B-subpairs are real. The involution module of G arises from the conjugation action of G on its involutions. We outline how (D. E) influences the vertices of components of the involution module that belong to B. These results allow us to enumerate the Frobenius-Schur indicators of the irreducible characters in B, where B has a dihedral defect group. The answer depends both on the decomposition matrix of B and on a defect couple of B. We also determine the vertices of the components of the involution module of B. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free