p. 223 - 233 Special representations of the Borel and maximal parabolic subgroups of G2(q) M. Ghorbany Received: April 6, 2008; Revised: December 8, 2008; Accepted: December 15, 2008 Abstract. A square matrix over the complex field with a non-negative integral trace is called a quasi-permutation matrix. For a finite group G, the minimal degree of a faithful representation of G by quasi-permutation matrices over the complex numbers is denoted by c(G), and r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper c(G) and r(G) are calculated for the Borel and maximal parabolic subgroups of G2(q). Keywords: Borel and parabolic subgroups; rational valued character; quasi-permutation representations. AMS Subject classification: Primary: 20C15. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |