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Remarks on Affine Springer Fibres
by G. Lusztig

Vol. 15 No. 1 (2020) P.1~P.8
 DOI: https://doi.org/10.21915/BIMAS.2020101 10.21915/BIMAS.2020101

ABSTRACT

Let h be a regular semisimple element in a complex simple Lie algebra $\frak g$. Let $\frak t$ be an indeterminate. We consider the “variety” of Iwahori subalgebras of $\frak g$ tensored with the power series in $\frak t$ which contain $\frak t$ times h. This variety admits a free action of a free abelian group of rank equal to the rank of $\frak g$. We describe a fundamental domain for this action.

KEYWORDS
Simple Lie algebra, Iwahori subalgebra, fundamental domain

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20G99

MILESTONES