Indicators of bismash products from exact symmetric group factorizations. Issue 10 (3rd October 2017) - Timmer, Joseph
ABSTRACT: We prove that all irreducible representations of the bismash productH = 𝕜 G # 𝕜 S n − k have Frobenius–Schur indicators +1 or 0 where 𝕜 is an algebraically closed field andS n = S n − k ⋅ G is an exact factorization. Moreover, we have a description of those simple modules which are not self-dual. We prove some new results for bismash products in general and make conjectures about bismash products that arise from other exact factorizations of S n .