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...

Every equivalence relation can be made into a groupoid with the same underlying set if we define the multiplication as follows: xy = x if x, y are related; otherwise, xy = y. The groupoids, obtained in this way, are called equivalence algebras. We find a finite base for the equations of equivalence algebras. The base consists of equations in four variables, and we prove that there is no base co...

We prove a bijection between finite-dimensional irreducible modules for an arbitrary quantum affine algebra Uq(g) and finite-dimensional irreducible modules for its Borel subalgebra Uq(g) ≥0.

For a finitely generated /̂ -algebra A and a finite dimensional ^-vector space M the representations of A on M form an affine ^-scheme Mod^(M). Of particular interest for this scheme are the connected components, the irreducible components, and the open and closed orbits under the natural action of the general linear group AutA(M), since the orbits are the equivalence classes of representations....

It has been conjectured that the group algebra Q[G] of a discrete group G over the rational numbers Q is semi-simple. In this paper we consider irreducible representations of this algebra satisfying certain finiteness conditions and see just how much information these yield towards solving the above problem. We show in fact for a finitely generated group G, Q[G] has "enough" of these representa...

The Lascoux-Leclerc-Thibon conjecture, reformulated and solved by S. Ariki, asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra g where g is gl ∞ or the affine Lie algebra A (1) l , and the irreducible representations correspond to the upper g...

Let V be a simple vertex operator algebra and let G be a finite automorphism group of V . In [DY], it was shown that any irreducible V -module is a completely reducible V module where V G is the G-invariant sub-vertex operator algebra of V . In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V...

We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field. We prove that any irreducible representation of the algebra is unitary equivalent ...

The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard q-deformation U ′ q(son) (which does not coincide with the Drinfel’d-Jimbo quantum algebra Uq(son)) of the universal enveloping algebra U(son(C)) of the Lie algebra son(C) when q is not a root of unity. These representations are exhausted by irreducible representations...