In a previous article, we have proved a result asserting the existence of a compatible family of Galois representations containing a given crystalline irreducible odd two-dimensional representation. We apply this result to establish new cases of the Fontaine-Mazur conjecture, namely, an irreducible Barsotti-Tate λ-adic 2-dimensional Galois representation unramified at 3 and such that the traces...

As further generalizations of Uq(sl2), an interesting class of algebras Uq(f(K,H)) was introduced and studied in [10]. In this paper, we further study these algebras by realizing them as Hyperbolic algebras. Such a realization yields a natural construction of interesting families of irreducible representations of Uq(f(K,H)) by using methods in non-commutative algebraic geometry([16]). We also i...

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...

Using a unified and systematic scheme, the free field realization of irreducible representations of osp(2|2) is constructed. The q-analogy of this unified scheme is used to construct q-free field realization of irreducible representations of U q (osp(2|2)). By using these realization, the correlation functions of N = 2 super-conformal (q-super-conformal) models based on osp(2|2) (U q (osp(2|2))...

The first two papers of this series1 were primarily concerned with a closure operation on the lattice of right ideals of a ring and the resulting direct-sum representation of the ring in case the closure operation was atomic. These results generalize the classical structure theory of semisimple rings. The present paper studies the irreducible components encountered in the direct-sum representat...

Let G be a connected, simply-connected, almost simple algebraic group of simplylaced type over C and let σ be a diagram automorphism of G. Let Gσ = ((G)) be the L-dual of the fixed point subgroup of σ on the L-dual of G. In this paper we relate the character of a finite dimensional irreducible representation of the disconnected algebraic group G〈σ〉 (generated by G and σ) on the connected compon...

where the Hilbert space direct sum is over all irreducible representations of G. Under the left action of G, the infinite dimensional representation on L(G) breaks up into finite dimensional representation spaces Vπ with multiplicity dim Vπ. What the Peter-Weyl theorem doesn’t do is tell us what the representations are and how to tell them apart. We would like to know how to project from L(G) o...

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 an 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 unitarily equiva...

We have seen that irreducible representations of a compact Lie group G can be constructed starting from a highest weight space and applying negative roots to a highest weight vector. One crucial thing that this construction does not easily tell us is what the character of this irreducible representation will be. The character would tell us not just which weights occur in the representation, but...