This report presents a new analytic method for checking the Schur stability of interval polynomial matrix (polynomials whose coefficients are interval matrices). In the suggested method, the interval Markov matrices of the interval polynomial matrix are used to assess its stability. The validity of the suggested method is illustrated through numerical examples. The proposed technique is algebra...

In this paper we are concerned with the problem of determining the character values and Schur indices of a finite group of Lie type over Fq. We show that (under some conditions on q) these values lie in the ring of algebraic integers generated by (1 + ñq)/2 and roots of unity of order prime to q. Furthermore, we determine the Schur indices for some of the (nonrational) unipotent characters in ...

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

New Schur stability checking method of the polynomial matrices whose coefficient matrix are interval matrices is presented in this paper. In the suggested method, the interval Markov matrices of the interval polynomial matrix are used to assess its stability. The validity of the suggested methods is illustrated through numerical examples. The main contribution of the suggested method is that it...

We study the notion of essential dimension for a linear representation of a finite group. In characteristic zero we relate it to the canonical dimension of certain products of Weil transfers of generalized Severi-Brauer varieties. We then proceed to compute the canonical dimension of a broad class of varieties of this type, extending earlier results of the first author. As a consequence, we pro...