A classical result in combinatorial representation theory states that irreducible characters of general linear groups may be defined as a sum over semi-standard Young tableaux. It turns out that a generating function due to Tokuyama, which recovers a deformation of the Weyl character formula, can be expressed in a similar spirit. In this talk, we will explore the connection between different combinatorial interpretations of Tokuyama's formula and, in particular, introduce a type of statistical mechanical model known as the six-vertex, or "ice-type" models. Speaker(s): Yutong Li