Principal subspaces for quantum affine algebra $U_q(A_n^{(1)})$

TL;DR

This paper introduces quantum analogues of quasi-particles for principal subspaces of quantum affine algebra modules, establishing relations and combinatorial bases for specific highest weights.

Contribution

It develops quantum analogues of quasi-particles and derives relations and bases for principal subspaces in quantum affine algebra modules.

Findings

Quantum quasi-particles are introduced and related.

Combinatorial bases for principal subspaces are constructed.

Relations among quantum quasi-particles are established.

Abstract

We consider principal subspace W({\Lambda}) of integrable highest weight module L({\Lambda}) for quantum affine algebra $U_q(\hat{\mathfrak{sl}}_{n+1})$. We introduce quantum analogues of the quasi-particles associated with the principal subspaces for $\hat{\mathfrak{sl}}_{n+1}$ and discover certain relations among them. By using these relations we find, for certain highest weight {\Lambda}, combinatorial bases of principal subspace W({\Lambda}) in terms of monomials of quantum quasi-particles.