An exact S-matrix is conjectured for the imaginary coupled d (3) 4 affine Toda field theory, using the U q (g (1) 2) symmetry. It is shown that this S-matrix is consistent with the results for the case of real coupling using the breather-particle correspondence. For q a root of unity it is argued that the theory can be restricted to yield Φ(11|14) perturbations of W A 2 minimal models and the r...

Let / be a prime number and m a divisor of /— 1. Then the Gauss period w = f + Çx + if +•■• + {/* , where ( = e2n'll and A is a primitive wth root of unity modulo /, generates a subfield K of Q(f ) of degree (/ 1)1 m . In this paper we study the reciprocal minimal polynomial Fi,m(X) = NK/q(1 ojX) of (w over Q. It will be shown that for fixed m and every N we have FLm(X) = (Bm(X)'/(l mX))l/m (mo...

A mixed graph D is a that can be obtained from by orienting some of its edges. Let α primitive n th root unity, then the α−Hermitian adjacency matrix defined to Hα = [hrs] where hrs if rs an arc in D, sr 1 digon and 0 otherwise. In this paper we study cospectrality Hermitian graph.

Let S(Λ) be the cyclotomic q-Schur algebra associated to the ArikiKoike algebra H . We construct a certain subalgebra S(Λ) of S(Λ), and show that it is a standardly based algebra in the sense of Du and Rui. S(Λ) has a natural quotient S(Λ), which turns out to be a cellular algebra. In the case where the modified Ariki-Koike algebra H ♭ is defined, S(Λ) coincides with the cyclotomic q-Schur alge...

Let F q be the finite field of q elements with characteristic p and F q m its extension of degree m. Fix a nontrivial additive character ψ of F p. For any Laurent polynomial −1 n ], we form the exponential sum S * m (f) := The corresponding L-function L * (f, t) is defined by L * (f, t) := exp (∞ ∑ m=0 S * m (f) t m m). The corresponding L-function L(f, t) is defined as follows L(f, t) := exp (...

Introduction. In the papers [DK1-2],[DKP1-2] the quantized enveloping algebras introduced by Drinfeld and Jimbo have been studied in the case q = ε, a primitive l-th root of 1 with l odd (cf. §2 for basic definitions). Let us only recall for the moment that such algebras are canonically constructed starting from a Cartan matrix of finite type and in particular we can talk of the associated clas...

We discuss the converse of a theorem of Potter stating that if the matrix equation AB = ωBA is satisfied with ω a primitive qth root of unity, then Aq+Bq = (A+B)q. We show that both conditions have to be modified to get a converse statement and we present a characterization when the converse holds for these modified conditions and q = 3 and a conjecture for the general case. We also present som...

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 fai...