Indicators of bismash products from exact symmetric group factorizations. Issue 10 (3rd October 2017)

• Record Type: Journal Article
• Authors: Timmer, Joseph
• Is Part Of: Communications in algebra. Volume 45:Issue 10(2017)
• Page Start: 4444
• Page End: 4465
• Publication Date: 2017-10-03
• Subjects: Hopf algebras -- representations -- symmetric group; 16T05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1270291
• Languages: English
• ISSNs: 0092-7872

Abstract

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 .