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

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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.

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Authors and Affiliations

  1. University of Southern California, Los Angeles, CA, 90089-1113, USA

    Andrea Jedwab & Susan Montgomery

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  1. Andrea Jedwab
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  2. Susan Montgomery
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Correspondence to Susan Montgomery.

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Both authors were supported by NSF grants DMS-07-01291 and DMS-04-01399.

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Jedwab, A., Montgomery, S. Representations of Some Hopf Algebras Associated to the Symmetric Group S n . Algebr Represent Theor 12, 1–17 (2009). https://doi.org/10.1007/s10468-008-9099-0

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  • DOI: https://doi.org/10.1007/s10468-008-9099-0

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