PBW bases and marginally large tableaux in types B and C

TL;DR

This paper establishes an explicit isomorphism between two combinatorial models of Kashiwara's infinity crystal in types B and C, involving marginally large tableaux and Kostant partitions from PBW bases, with a simplified stack notation.

Contribution

It provides a new explicit description of the isomorphism between combinatorial realizations of Kashiwara's crystal in types B and C, introducing a stack notation for Kostant partitions.

Findings

Explicit isomorphism between marginally large tableaux and Kostant partitions.

Introduction of a stack notation simplifying Kostant partition realization.

Enhanced understanding of crystal structures in types B and C.

Abstract

We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara's infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from PBW bases. We also discuss a stack notation for Kostant partitions which simplifies that realization.