The quantum group $\dot U$ and flag manifolds over the semifield Z

TL;DR

This paper introduces a parametrization of the canonical basis of a modified quantum group using the flag manifold over the semifield Z, linking algebraic structures to geometric objects.

Contribution

It provides a novel parametrization of the canonical basis of quantum groups via flag manifolds over the semifield Z, enhancing understanding of their structure.

Findings

Parametrization of the canonical basis in terms of flag manifolds over Z

Correction of minor errors in previous formulations

Connection established between quantum groups and geometric flag varieties

Abstract

We give a parametrization of the canonical basis of the modified quantum group corresponding to a root datum in terms of the flag manifold over the semifield Z associated to the reductive group corresponding to the dual root datum. Some minor errors corrected.