2017/05/19 by Alexandre Zalesski, Zalesski, Alexandre · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1705.07179
openalex publication_date 2017/05/19 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We study the decomposition of certain reducible characters of classical\ngroups as the sum of irreducible ones. Let mathbf G be an algebraic group\nof classical type with defining characteristic p>0, \μ a dominant weight\nand W the Weyl group of mathbf G. Let G=G(q) be a finite classical\ngroup, where q is a p-power. For a weight \μ of mathbf G the sum\ns_\μ of distinct weights w(\μ) with w\∈ W viewed as a function on the\nsemisimple elements of G is known to be a generalized Brauer character of G\ncalled an orbit character of G. We compute, for certain orbit characters and\nevery maximal torus T of G, the multiplicity of the trivial character 1T\nof T in s_\μ. The main case is where \μ=(q-1)\ω and \ω is a\nfundamental weight of mathbf G. Let St denote the Steinberg character of\nG. Then we determine the unipotent characters occurring as constituents of\ns_\μ\⋅ St defined to be 0 at the p-singular elements of G. Let\n\β_\μ denote the Brauer character of a representation of SLn(q)\narising from an irreducible representation of mathbf G with highest weight\n\μ. Then we determine the unipotent constituents of the characters\n\β_\μ\⋅ St for \μ=(q-1)\ω, and also for some other \μ\n(called strongly q-restricted). In addition, for strongly restricted weights\n\μ, we compute the mult of 1T in the restriction \β_\μ|T for\nevery maximal torus T of G.\n