Frobenius-Schur indicators of characters in blocks with cyclic defect

Abstract

Consider a real block with cyclic defect of a finite group for an odd prime. We show that the exceptional characters have the same Frobenius-Schur indicators. Moreover the common value can be computed using the canonical character of the block. We also prove some results about the Frobenius-Schur indicators of the non-exceptional characters.If a finite group has cyclic Sylow p-subgroups, where p is an odd prime, we show that the number of irreducible characters with Frobenius-Schur indicator −1 is greater than or equal to the number of conjugacy classes of weakly real p-elements.