Word reading is a crystal morphism

TL;DR

This paper demonstrates that word reading functions as a crystal morphism and proves that, for the complex special linear group, the map from galleries to MV cycles preserves crystal structure.

Contribution

It introduces the concept of word reading as a crystal morphism and establishes the morphism property for galleries and MV cycles in the complex special linear group.

Findings

Word reading is a crystal morphism.

The map from galleries to MV cycles is a crystal morphism for SL.

Theoretical framework connecting galleries and MV cycles.

Abstract

We observe that word reading is a crystal morphism. This leads us to prove that, in the case of the complex special linear group, the map from all galleries to MV cycles is a morphism of crystals.