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

Murray, John (2009) Real Subpairs and Frobenius-Schur indicators of characters in 2-blocks. Journal of Algebra, 322 (2). pp. 489-513. ISSN 0021-8693

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Let B be a real 2-block of a finite group G. A defect couple of B is a certain pair (D,E) of 2-subgroups of G, such that D 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, when 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.

Item Type: Article
Keywords: Block; Dihedral defect group; Frobenius-Schur indicator, Extended defect group; Subpairs.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1787
Identification Number: 10.1016/j.jalgebra.2009.04.016
Depositing User: Dr. John Murray
Date Deposited: 19 Jan 2010 12:49
Journal or Publication Title: Journal of Algebra
Publisher: Elsevier
Refereed: Yes

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