Completed Iwahori–Hecke algebra for Kac–Moody groups over local fields
Abstract
Abstract Let be a split Kac–Moody group over a non‐Archimedean local field, and let be the Iwahori–Hecke algebra of . In this paper, we construct a completed Iwahori–Hecke algebra and prove that it contains a large center isomorphic to Looijenga's invariant ring. By the Kac–Moody Satake isomorphism, Looijenga's invariant ring is isomorphic to the spherical Hecke algebra. We prove that our completion is equal to Iwahori biinvariant functions on satisfying a support condition that we call Weyl almost finite support .
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic structures and combinatorial models
Advanced Operator Algebra Research
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Volume
- 133
- Issue
- 2
- Publication date
- 1 August 2026
- Language
- EN