Partial flag manifolds over a semifield

TL;DR

This paper introduces a new way to define partial flag manifolds over a semifield using canonical bases, extending classical concepts to a broader algebraic setting.

Contribution

It provides the first construction of K-forms of partial flag manifolds over semifields for simply laced semisimple groups, linking algebraic geometry and canonical basis theory.

Findings

Defines K-forms of partial flag manifolds over semifields

Establishes a connection between canonical bases and algebraic structures over semifields

Extends classical flag manifold theory to new algebraic contexts

Abstract

For any semifield K we define a K-form of a partial flag manifold of a semisimple group G of simply laced type over the complex numbers. The definition is in terms of the theory of canonical bases.