Girstmair in [1, Theorem 1] gave a generalization of Murty's irreducibility criterion (see [2, 1]). In this article, we further generalize these criteria.

In this note, we present two new identities for derangements. As a corrolary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.

A bstract . We consider cooperative, uniformly elliptic systems, with bounded coefficients and coupling in the zeroth-order terms. We establish two analogues of Harnack’s inequality for this class of systems: A weak version is obtained under fairly general conditions, while imposing an irreducibility condition on the coupling coefficients we obtain a stronger version of the inequality. This irr...

Standard results in general equilibrium theory, such as existence and the second efficiency and core equivalence theorems, are most easily proved for compensated equilibria. A new condition establishes that, even with individual non-convexities, in compensated equilibrium any agent with a cheaper feasible net trade is also in uncompensated equilibrium. Some generalizations of McKenzie’s irreduc...

We consider the energy representation for the gauge group. The gauge group is the set of C∞mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy representation of the gauge group for any dimension of M . To prove irreducibility for the energy representation, we use the fact that each operator from a space of test fu...

The concept of irreducibility in shop scheduling problems withdifferent objectives has proven one of the most fertile research topics as theset of all irreducible sequences in a given shop contains at least one optimalsequence for arbitrary processing times. Recently, a number of equivalent for-mulations of the reducibility in open-shop problem with Makespan objectivesare pr...

The idea of looking at the prime factorization of the coefficients of a polynomial in Z[x] in order to establish its irreducibility (over Q) goes back to the classical Schönemann-Eisenstein criterion first derived in [29] and [6] in the middle of the 19th century. At the beginning of the 20th century, G. Dumas [5], again making use of primes that divide the coefficients of a polynomial, introdu...

In this note, we show that if the characteristic polynomial of some Hecke operator Tn acting on the space of weight k cusp forms for the group SL2(Z ) is irreducible, then the same holds for Tp, where p runs through a density one set of primes. This proves that if Maeda’s conjecture is true for some Tn, then it is true for Tp for almost all primes p.

Irreducible representations are the building blocks of general, semisimple Galois representations ρ, and cuspidal representations are the building blocks of automorphic forms π of the general linear group. It is expected that when an object of the former type is associated to one of the latter type, usually in terms of an identity of L-functions, the irreducibility of the former should imply th...

We propose the following computational assumption: in general if we try to compress the depth of a circuit family (parallel time) more than a constant factor we will suffer super-quasipolynomial blowup in the size (number of processors). This assumption is only slightly stronger than the popular assumption about the robustness of NC, and we observe that it has surprising consequences. Note also...