## Deformations of the Weyl Character Formula for $SO(2n+1,\mathbb{C})$ via Ice Models. (arXiv:1811.11879v1 [math.CO])

We explore combinatorial formulas for deformations of highest weight
characters of the odd orthogonal group $SO(2n+1)$. Our goal is to represent
these deformations of characters as partition functions of statistical
mechanical models -- in particular, two-dimensional solvable lattice models. In
Cartan type $A$, Hamel and King [8] and Brubaker, Bump, and Friedberg [3] gave
square ice models on a rectangular lattice which produced such a deformation.
Outside of type $A$, ice-type models were found using rectangular lattices with
additional boundary conditions that split into two classes -- those with
`nested' and `non-nested bends.' Our results fill a gap in the literature,
providing the first such formulas for type $B$ with non-nested bends. In type
$B$, there are many known combinatorial parameterizations of highest weight
representation basis vectors as catalogued by Proctor [19]. We show that some
of these permit ice-type models via appropriate bijections (those of Sundaram
[21] and查看全文