2022/08/22 by Kayla Orlinsky, Orlinsky, Kayla
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2208.12714
openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The semisimple bismash product Hopf algebra Jn=k^Sn-1#kCn for an algebraically closed field k is constructed using the matched pair actions of Cn and Sn-1 on each other. In this work, we reinterpret these actions and use an understanding of the involutions of Sn-1 to derive a new Froebnius-Schur indicator formula for irreps of Jn and show that for n odd, all indicators of Jn are nonnegative. We also derive a variety of counting formulas including Theorem 6.2.2 which fully describes the indicators of all 2-dimensional irreps of Jn and Theorem 6.1.2 which fully describes the indicators of all odd-dimensional irreps of Jn and use these formulas to show that nonzero indicators become rare for large n.