TY - JOUR

T1 - Real Blocks with Dihedral Defect Groups Revisited

AU - Sambale, Benjamin

N1 - Funding Information: This work is supported by the German Research Foundation (SA 2864/4-1).

PY - 2024/4

Y1 - 2024/4

N2 - The Frobenius–Schur indicators of characters in a real 2-block with dihedral defect groups have been determined by Murray [‘Real subpairs and Frobenius–Schur indicators of characters in 2-blocks’, J. Algebra 322 (2009), 489–513]. We show that two infinite families described in his work do not exist and we construct examples for the remaining families. We further present some partial results on Frobenius–Schur indicators of characters in other tame blocks.

AB - The Frobenius–Schur indicators of characters in a real 2-block with dihedral defect groups have been determined by Murray [‘Real subpairs and Frobenius–Schur indicators of characters in 2-blocks’, J. Algebra 322 (2009), 489–513]. We show that two infinite families described in his work do not exist and we construct examples for the remaining families. We further present some partial results on Frobenius–Schur indicators of characters in other tame blocks.

KW - dihedral defect groups

KW - Frobenius–Schur indicator

KW - real blocks

UR - http://www.scopus.com/inward/record.url?scp=85162139291&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2304.14639

DO - 10.48550/arXiv.2304.14639

M3 - Article

AN - SCOPUS:85162139291

VL - 109

SP - 327

EP - 341

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 2

ER -