Quasi-permutation Representations of Borel and Parabolic Subgroups of Steinberg's triality groups

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 2، شماره 1 - شماره پیاپی 2، فروردین 2009   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v2i1.637

نویسنده

M. Ghorbany^*

Iran University of Science and Tecnology, Mazandaran

چکیده

If G is a finite linear group of degree n, that is, a finite group of automor-phisms of an n-dimensional complex vector space, or equivalently, a finite group of non-singular matrices of order n with complex coefficients, we shall say that G is a quasi-permutation group if the trace of every element of G is a non-negative rational integer. By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace.
Thus every permutation matrix over C is a quasi-permutation matrix. For a given finite group G, let c(G) denote the minimal degree of a faithful rep-resentation of G by quasi-permutation matrices over the complex numbers and let r(G) denote the minimal degree of a faithful rational valued complex character of G. The purpose of this paper is to calculate c(G) and r(G) for
the Borel and parabolic subgroups of Steinberg's triality groups.

کلیدواژه‌ها

Borel subgroup؛ character table, parabolic subgroup؛ quasi-permutation؛ Steinberg's triality group