2015/02/05 by Carlos A. M. André, André, Carlos A. M., Pedro J. Freitas +3
Mathematics · #20C15 #20D15 #20G40 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C15 #msc:20D15 #msc:20G40
paper · pdf · doi:10.48550/arxiv.1502.01512
Accepted for publication in the Journal of Algebra. arXiv admin note: text overlap with arXiv:1201.1060 by other authors
arxiv created 2015/02/05 · arxiv updated 2015/02/06
If \mathscrJ is a finite-dimensional nilpotent algebra over a finite field \Bbbk, the algebra group P = 1+\mathscrJ admits a (standard) supercharacter theory as defined by Diaconis and Isaacs. If \mathscrJ is endowed with an involution \widehatς, then \widehatς naturally defines a group automorphism of P = 1+\mathscrJ, and we may consider the fixed point subgroup CP(\widehatς) = \x∈ P : \widehatς(x) = x-1\. Assuming that \Bbbk has odd characteristic p, we use the standard supercharacter theory for P to construct a supercharacter theory for CP(\widehatς). In particular, we obtain a supercharacter theory for the Sylow p-subgroups of the finite classical groups of Lie type, and thus extend in a uniform way the construction given by André and Neto for the special case of the symplectic and orthogonal groups.