Peer-Reviewed Journal Details
Mandatory Fields
Murray, J
2009
July
Journal of Algebra
Real subpairs and Frobenius-Schur indicators of characters in 2-blocks
Published
3 ()
Optional Fields
DIHEDRAL DEFECT-GROUPS FINITE-GROUPS PROJECTIVE-MODULES BLOCKS REPRESENTATIONS ALGEBRAS
322
489
513
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.
SAN DIEGO
0021-8693
10.1016/j.jalgebra.2009.04.016
Grant Details