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We first characterize the increasing eigenfunctions associated to the following family of integro-differential operators, for any α, x>0, γ≥0 and fa smooth function on ,
where the coefficients ,σ≥0 and the measure ν, which satisfies the integrability condition ∫0∞(1∧r2)ν(dr)<+∞, are uniquely determined by the distribution of a spectrally negative, infinitely divisible random variable, with characteristic exponent ψ. L(γ) is known to be the infinitesimal generator of a positive...
A fairly old problem in modular representation theory is to determine the vanishing behavior of the groups and higher groups of Weyl modules and to compute the dimension of the -vector space for any partitions , of , which is the intertwining number. K. Akin, D. A. Buchsbaum, and D. Flores solved this problem in the cases of partitions of length two and three. In this paper, we describe the vanishing behavior of the groups and provide a new formula for the intertwining number for any...
Let be any field of characteristic . It is well-known that there are exactly inequivalent indecomposable representations of defined over . Thus if is any finite dimensional -representation there are non-negative integers such that . It is also well-known there is a unique (up to equivalence) dimensional irreducible complex representation of given by its action on the space of forms. Here we prove a conjecture, made by R. J. Shank, which reduces the computation of the ring...
Let be a field of characteristic . Let be a finite group of order divisible by and a -Sylow subgroup of . We describe the kernel of the restriction homomorphism , for the group of endotrivial representations. Our description involves functions that we call weak -homomorphisms. These are generalizations to possibly non-normal of the classical homomorphisms appearing in the normal case.
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