Systems of parameters and holonomicity of A-hypergeometric systems

Abstract

Abstract. The main result is an elementary proof of holonomicity for A-hypergeometric systems, with no requirements on the behavior of their singularities, originally due to Adolphson [Ado94] after the regular singular case by Gelfand and Gelfand [GG86]. Our method yields a direct de novo proof that A-hypergeometric systems form holonomic families over their parameter spaces, as shown by Matusevich, Miller, and Walther [MMW05].

Unitary Representations of Cyclotomic Hecke Algebras at Roots of Unity: Combinatorial Classification and BGG Resolutions

“…In the case of the unitary representations of the Hecke algebra of the symmetric group, the resolutions of Theorem C were the subject of the authors’ previous work [13] and Theorem C reproves a conjecture of Berkesch–Griffeth–Sam [7]. Theorem C vastly generalises this work to all unitary representations of all cyclotomic Hecke algebras.…”