On Sharifi’s conjecture: Exceptional case

A Conjecture on Exceptional Orthogonal Polynomials

Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials introduced by Cariñena et al., [3]. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical...

On the Geometry of Thin Exceptional Sets in Manin’s Conjecture

Manin’s Conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set. We study whether the exceptional set in Manin’s Conjecture is a thin set.

Restricted set addition: The exceptional case of the Erdos-Heilbronn conjecture

Exceptional case studies.

CASE STUDIES ARE RARE in our journals and for good reason: without a sample, it is hard to assess the representativeness or uniqueness of an individual. The case studies that do get published are therefore so obviously exceptional that we cannot help but be interested in where nature or nurture has taken one of our species. The individual is usually an athlete, and the science amounts to identi...

James’ Conjecture for Hecke algebras of exceptional type, I

In this paper, and a second part to follow, we complete the programme (initiated more than 15 years ago) of determining the decomposition numbers and verifying James’ Conjecture for Iwahori–Hecke algebras of exceptional type. The new ingredients which allow us to achieve this aim are: • the fact, recently proved by the first author, that all Hecke algebras of finite type are cellular in the sen...