On Linear Hodge Newton Decomposition for Reductive Monoids

摘要

Let F be the field of fractions of a complete discrete valuation ring o. Let G be an irreducible linear reductive monoid over F, such that its group G of units is split over o. When G is either a connected reductive o-split linear algebraic group over F or the monoid of n x n matrices over F, Kottwitz and Viehmann had proved a relation between the Hodge point and the Newton point associated to an element γ ? G(F). Suppose F has characteristic zero. In [7], we had given a monoid theoretic generalization of this phenomenon. On the way, we had applied the Putcha-Renner theory of linear algebraic monoids over algebraically closed fields to study G(F) by generalizing various results for linear algebraic groups over F such as the Iwasawa, Cartan and affine Bruhat decompositions. In this article we give an exposition of these results.