Similarity and Kirillov-Schilling-Shimozono bijection

TL;DR

This paper investigates the Kirillov-Schilling-Shimozono bijection's behavior under similarity maps on crystals, extending its definition to rational numbers and proposing conjectures for real number extensions.

Contribution

It introduces a method to extend the bijection to rational numbers and explores conjectures for further extension to real numbers.

Findings

Bijection behavior under similarity maps analyzed

Extension of bijection to $ ext{Q}$ demonstrated

Conjectures for extension to $ ext{R}$ proposed

Abstract

The behavior of the Kirillov-Schilling-Shimozono bijection is examined under the similarity map on Kirillov-Reshetikhin crystals. It enables us to define this bijection over $\mathbb{Q}$. Conjectures on the extension to $\mathbb{R}$ is also presented.