A 3-connected quadrangulation of a closed surface is said to be K′ 3-irreducible if no faceor cube-contraction preserves simplicity and 3-connectedness. In this paper, we prove that a K′ 3-irreducible quadrangulation of a closed surface except the sphere and the projective plane is either (i) irreducible or (ii) obtained from an irreducible quadrangulation H by applying 4-cycle additions to F0 ...

The goal of this paper is to study the irreducible representations of semisimple Lie algebras. We will begin by considering two cases of such algebras: sl2(C) and sl3(C). First, we discover the irreducible representations of sl2(C). The process used in doing so will guide us through our development of the irreducible representations of sl3(C). We will note several key similarities in the proces...

Given a numerical approximation to a point p on the set V of common zeroes of a set of multivariate polynomials with complex coefficients, this article presents an efficient method to compute the maximum dimension of the irreducible components of V which pass through p, i.e., a local dimension test. Such a test, used to filter out the so-called “junk points,” is a crucial element in the numeric...

Besides Karatsuba algorithm, optimal Toeplitz matrix-vector product (TMVP) formulae is another approach to design GF (2) subquadratic multipliers. However, when GF (2) elements are represented using a shifted polynomial basis, this approach is currently appliable only to GF (2)s generated by all irreducible trinomials and a special type of irreducible pentanomials, not all general irreducible p...

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...

Branching of symplectic groups is not multiplicity-free. We describe a new approach to resolving these multiplicities that is based on studying the associated branching algebra B. The algebra B is a graded algebra whose components encode the multiplicities of irreducible representations of Sp2n−2 in irreducible representations of Sp2n. Our rst theorem states that the map taking an element of Sp...

This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset˜Ω. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield...

The following propositions are true: (1) For every sup-semilattice L and for all elements x, y of L holds ⌈⌉L(↑x∩ ↑y) = x ⊔ y. (2) For every semilattice L and for all elements x, y of L holds ⊔ L(↓x∩↓y) = x ⊓ y. (3) Let L be a non empty relational structure and x, y be elements of L. If x is maximal in (the carrier of L) \ ↑y, then ↑x \ {x} = ↑x ∩ ↑y. (4) Let L be a non empty relational structu...

For each connected real semisimple matrix group, one obtains a constructive list of the irreducible tempered unitary representations and their characters. These irreducible representations all turn out to be instances of a more general kind of representation, here called basic. The result completes Langland's classification of all irreducible admissible representations for such groups. Since no...

An operator is said to be strongly irreducible if its commutant has no nontrivial idempotent. This paper first shows that if an operator is not strongly irreducible then the set of idempotents in its commutant is either finite or uncountable. The second part of the paper focuses on the Jordan block which is a well-known class of irreducible operators, and determines when a Jordan block is stron...