Let there be given n ordinals cti, alt • • • , an. It is well known that every ordinal can be written uniquely as the sum of indecomposable ordinals. (An ordinal is said to be indecomposable if it is not the sum of two smaller ordinals.) Denote by (ct...

We prove that under some assumptions on an algebraic group G, indecomposable direct summands of the motive of a projective G-homogeneous variety with coefficients in Fp remain indecomposable if the ring of coefficients is any field of characteristic p. In particular for any projective G-homogeneous variety X, the decomposition of the motive of X in a direct sum of indecomposable motives with co...

We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and a further one with a link pattern Hamiltonian, can be understood as arising from different representations of the one-boundary Temperley–Lieb algebra. For a system of size L these representations a...

A tournament is acyclically indecomposable if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The profile of a tournament T is the function φT which counts for each integer n the n...

We give a new approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and of Schur functions. We consider the set of probability distributions as a semigroup M equipped with the operation of free convolution and prove a Khintchine type theorem for factorization of elements of this semigroup. Any element of M contains either indecomp...

Let there be given n ordinals al, a2, • • • , an . It is well known that every ordinal can be written uniquely as the sum of indecomposable ordinals. (An ordinal is said to be indecomposable if it is not the sum of two smaller ordinals .) Denote by ¢(a) the largest of these indecomposable ordinals belonging to a . (4(a) may have a coefficient c in the decomposition of a.) Put y=minis . 0(ai), a...

1. Introduction LET 0 be a finite group. If p is a prime which, divides the order of G, there exists in general an infinite number of indecomposable representations of 0 over a field of characteristic p. We are concerned here with the in-decomposable representations of a group G which is an extension of a 2?-nilpotent"f group by a cyclic group of order prime to p. We reduce the study of these r...