where ε = μq, ε p q = μp. The systems for which small parameter has a fractional power were studied by V.K. Grigorenko in [1]. The case of the simple roots of the characteristic equations and the case of the equation having only one multiple n root were studied separately. Let us construct the asymptotic solution of the system (1) by the method of perturbed characteristic equation [2] for the c...

Let H n be the Iwahori-Hecke algebra of type A n?1. For each Young diagram , an H n module S , called a Specht module, was deened in DJ]. The dimension of S does not depend on the choice of q, and for q not a root of unity, the S 's provide a complete set of irreducible H n-modules, up to isomorphism. If q is a primitive l-th root of unity, a complete set of simple H n-modules (D) has been cons...

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 quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

1. Let A = [aii] be an n-th order irreducible non-negative matrix. As is very well-known, the matrix A has a positive characteristic root p (provided that n> I), which is simple and maximal in the sense that every characteristic root A satisfies I A I ~ p, and the characteristic vector x belonging to p may be chosen positive. These results, originally due to Frobenius, have been proved by Wiela...

We compute the center in case q is a primitive root of unity. 1. Introduction Let F be a eld of characteristic zero. There are several ways to quantize the matrix algebra M n (F). Among them, the most common is probably the algebra introduced by Faddeev, Reshetikhin, and Takhtajan in 4]. Denote that algebra by M n (q). In 3] Dipper and Donkin deened another quantized matrix algebra which has ma...

Let g be a complex finite dimensional simple Lie algebra with the root datum (Y,X, . . . ), see [Lu2]. Let Wf denote the Weyl group, R denote the root system, R+ denote the set of positive roots. Let X+ denote the set of dominant integral weights. Let h denote the Coxeter number of g. Let us fix l ∈ N, l > h. We assume that l is odd (and not divisible by 3, if g is of type G2). Let W denote the...

Let X be a Hausdorff compact space and C(X) be the algebra of all continuous complex-valued functions on X, endowed with the supremum norm. We say that C(X) is (approximately) n-th root closed if any function from C(X) is (approximately) equal to the n-th power of another function. We characterize the approximate n-th root closedness of C(X) in terms of ndivisibility of first Čech cohomology gr...