2016/04/08 by Peter Schauenburg, Schauenburg, Peter
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1604.02378
openalex publication_date 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new approach to calculating the higher Frobenius-Schur indicators for the simple modules over the Drinfeld double of a finite group. In contrast to the formula by Kashina-Sommerhäuser-Zhu that involves a sum over all group elements satisfying a certain condition, our formula operates on the level of conjugacy classes and character tables. It can be implemented in the computer algebra system GAP, efficiently enough to deal, on a laptop, with symmetric groups up to S18 (providing further evidence that indicators are non-negative in this case) or simple groups of order up to 2 ⋅ 108. The approach also allows us to test whether all indicators over the double of a given group are rational , without computing them. Among simple groups of order up to about 5 ⋅ 1011 an inspection yields exactly one example (of order about 5 ⋅ 109) where irrational indicators occur.