Representations of Some Hopf Algebras Associated to the Symmetric Group S n期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Representations of Some Hopf Algebras Associated to the Symmetric Group S n

Authors:	Andrea Jedwab Susan Montgomery

Affiliation:	(1) University of Southern California, Los Angeles, CA 90089-1113, USA

Abstract:	We prove that all irreducible representations of the bismash product $H_n = k^{C_n } # kS_{n - 1}$ have Frobenius–Schur indicator +1, where k is an algebraically closed field of characteristic 0. If n = p, a prime, we find all indicators for $J_n = k^{S_{n - 1} } # k^{C_n }$ . We also study more general bismash products. Both authors were supported by NSF grants DMS-07-01291 and DMS-04-01399.

Keywords:	Hopf algebras Symmetric group S _n Frobenius– Schur indicators
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