Tuesday, February 8, 2022 2:00 PM
Slava Naprienko

Seminar page.

I will review two well-known integrability classes of the six-vertex model and introduce their generalizations.

The field-free class with a1=a2, b1=b2, c1=c2. The partition function is given by the Izergin-Korepin determinant. The homogeneous limit of the determinant gives the enumeration of the alternating sign matrices and refinements. I extend the class to b1 != b2 and show that the generalized Izergin-Korepin determinant holds.

The free-fermionic class with parameter a1a2 + b1b2 = c1c2. The partition function gives the special functions: Schur polynomials, Spherical Whittaker functions, and refinements depending on the choice of weights. I compute the partition function for the generic free-fermionic weights. It has the form of the deformed Weyl denominator and Schur-like function.