Decorations on Geometric Crystals and Monomial Realizations of Crystal Bases for Classical Groups

TL;DR

This paper explicitly describes decoration functions for geometric crystals of classical groups and demonstrates their representation through monomial realizations of crystal bases.

Contribution

It provides an explicit description of decoration functions and links them to monomial realizations for classical groups' geometric crystals.

Findings

Decoration functions are explicitly described for certain geometric crystals.

Decoration functions are represented via monomial realizations of crystal bases.

The work enhances understanding of the structure of geometric crystals for classical groups.

Abstract

We shall describe explicitly the decoration functions for certain decorated geometric crystals of classical groups and we shall show that they are represented in terms of monomial realizations of crystal bases.