In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Br...

A problem naturally arizing in the unit-cost complexity class NP over the field of complex numbers consists in deciding if an input of length 2n belongs to a special absolutely irreducible hypersurface of the affine space 2n . Consequently, the decision problem is substituted by a computation problem.

let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...

In this paper, we describe a study into the explicit construction of irreducible representations of the Hecke algebra Hn(q) of type An−1 in the non-generic case where q is a root of unity. The approach is via the Specht modules of Hn(q) which are irreducible in the generic case, and possess a natural basis indexed by Young tableaux. The general framework in which the irreducible non-generic Hn(...

We consider the question: can the isotropy representation of an irreducible pseudoRiemannian symmetric space be realized as a conformal holonomy group? Using recent results of Čap, Gover and Hammerl, we study the representations of SO(2, 1), PSU(2, 1) and PSp(2, 1) as isotropy groups of irreducible symmetric spaces of signature (3, 2), (4, 4) and (6, 8), respectively, describing the geometry in...

‎let $g$ be a finite group‎. ‎an element $gin g$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $chi$ of $g$‎, ‎$chi(g)neq 0$‎. ‎the bi-cayley graph $bcay(g,t)$ of $g$ with respect to a subset $tsubseteq g$‎, ‎is an undirected graph with‎ ‎vertex set $gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin g‎, ‎ tin t}$‎. ‎let $nv(g)$ be the set‎ ‎of all non-vanishing element...

Abstract In this work, we prove a version of the Sylvester–Gallai theorem for quadratic polynomials that takes us one step closer to obtaining deterministic polynomial time algorithm testing zeroness $\Sigma ^{[3]}\Pi \Sigma \Pi ^{[2]}$ circuits. Specifically, that, if finite set irreducible ${\mathcal {Q}}$ satisfies every two $Q_1,Q_2\in {\mathcal there is subset {K}}\subset such $Q_1,Q_2 \no...

Let Amx„, Bmxn, Xnxl, and Ymxl be matrices whose entries are nonnegative real numbers and suppose that no row of A and no column of B consists entirely of zeroes. Define the operators U, T and T by (UX)t-X? [or (UY),= Y;1], T=UB'UA and T' = UAUB'. Tis called irreducible if for no nonempty proper subset S of (1, • ■ ■ , n} it is true that X,=0, ieS; X,^0, i$ S, implies (TX),=0, ieS; (TX)i^O, i $...