## Principal subspaces for quantum affine algebra $$U_q (\widehat{\mathfrak{sl}}_{n+1})$$
In this talk, we consider principal subspaces of the integrable highest weight $$U_q (\widehat{\mathfrak{sl}}_{n+1})$$-modules. We construct combinatorial bases of the principal subspaces, consisting of quasi-particle monomials acting on the highest weight vector, and discuss, for $$n=1$$, related constructions in terms of vertex operator monomials.