2022/10/27 by Réda Boumasmoud, Boumasmoud, Reda, Radhika Ganapathy +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Alkaloids: synthesis and pharmacology #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2210.15190
We describe the center of the Hecke algebra of a type attached to a Bernstein block under some hypothesis. When \bf G is a connected reductive group over non-archimedean local field F that splits over a tamely ramified extension of F and the residue characteristic of F does not divide the order of the absolute Weyl group of \bf G, the works of Kim-Yu and Fintzen associate a type to each Bernstein block and our hypothesis is satisfied for such types. We use our results to give a description of the Bernstein center of the Hecke algebra H(\bf G (F),K) when K belongs to a nice family of compact open subgroups of \bf G(F) (which includes all the Moy-Prasad filtrations of an Iwahori subgroup) via the theory of types.