Work

Completed Iwahori–Hecke algebra for Kac–Moody groups over local fields

Year: 2026

Type: article

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 .

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70189

Authors: Auguste Hébert, Dinakar Muthiah

Institutions: Institut Élie Cartan de Lorraine, Université de Lorraine, University of Glasgow

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Engineering and Physical Sciences Research Council, Japan Society for the Promotion of Science

Awards: Geometry of double loop groups, Loop and double loop geometry