Fock space representations of quantum affine algebras and generalized Lascoux-Leclerc-Thibon algorithm

TL;DR

This paper constructs Fock space representations of classical quantum affine algebras via Young walls, relates their crystal graphs to abstract crystals, and generalizes an algorithm for computing their global bases.

Contribution

It introduces a combinatorial approach using Young walls for Fock space representations and extends the Lascoux-Leclerc-Thibon algorithm for classical quantum affine algebras.

Findings

Fock space representations realized through Young walls

Crystal graphs correspond to proper Young walls

Generalized algorithm for global bases computation

Abstract

We construct the Fock space representations of classical quantum affine algebras using combinatorics of Young walls. We also show that the crystal graphs of the Fock space representations can be realized as the abstract crystal consisting of proper Young walls. Finally, we give a generalized version of Lascoux-Leclerc-Thibon algorithm for computing the global bases of the basic representations of classical quantum affine algebras.