Finiteness Theorems for Kac-Moody Groups Over Nonarchimedean Local Fields

2019/11/23 by Ali, Abid
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1911.10405

Abstract

We prove the finiteness of formal analogues of the spherical function (Spherical Finiteness), the \mathbf c-function (Gindikin-Karpelevich Finiteness), and obtain a formal analogue of Harish-Chandra's limit (Approximation Theorem) relating spherical and \mathbf c-function in the setting of p-adic Kac-Moody groups. The finiteness theorems imply that the formal analogue of the Gindikin-Karpelevich integral is well defined in local Kac-Moody settings. These results extend the Braverman-Garland-Kazhdan-Patnaik's affine Gindikin-Karpelevich finiteness theorems and provide an algebraic analogue of the geometrical results of Gaussent-Rousseau and Hébert.

Related

• An affine Gindikin-Karpelevich formula
• Finite presentability of Kac-Moody groups over finite fields
• Spherical Hecke algebras for Kac-Moody groups over local fields
• Kato's irreducibility criterion for Kac-Moody groups over local fields
• Elementary equivalence of Kac-Moody groups