AROUND THE LIE CORRESPONDENCE FOR COMPLETE KAC-MOODY GROUPS AND GABBER-KAC SIMPLICITY

Marquis T (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Annales de l'Institut Fourier Association des Annales de l'Institute Fourier; 1999

Book Volume: 69

Pages Range: 2519-2576

Journal Issue: 6

DOI: 10.5802/aif.3301

Abstract

Let k be a field and A be a generalised Cartan matrix, and let G(A)(k) be the corresponding minimal Kac-Moody group of simply connected type over k. Consider the completion G(A)(pma) (k) of G(A)(k) introduced by O. Mathieu and G. Rousseau, and let U-A(ma)+ (k) denote the unipotent radical of the Borel subgroup of G(A)(pma) (k). In this paper, we exhibit a functorial dependence of the groups U-A(ma+)(k) and G(A)(pma) ( k) ( on their Lie algebra. We also provide several contributions to fundamental questions in the general theory of maximal Kac-Moody groups: (non-)Gabber-Kac simplicity over certain finite fields, (non-)density of a minimal Kac-Moody group in its Mathieu-Rousseau completion, (non-)linearity of maximal pro-p subgroups, and the isomorphism problem.

Authors with CRIS profile

Timothée Marquis Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

How to cite

APA:

Marquis, T. (2019). AROUND THE LIE CORRESPONDENCE FOR COMPLETE KAC-MOODY GROUPS AND GABBER-KAC SIMPLICITY. Annales de l'Institut Fourier, 69(6), 2519-2576. https://dx.doi.org/10.5802/aif.3301

MLA:

Marquis, Timothée. "AROUND THE LIE CORRESPONDENCE FOR COMPLETE KAC-MOODY GROUPS AND GABBER-KAC SIMPLICITY." Annales de l'Institut Fourier 69.6 (2019): 2519-2576.

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