Super Rogers–Szegö polynomials associated with BCN type of Polychronakos spin chains

Abstract

As is well known, multivariate Rogers–Szegö polynomials are closely connected with the partition functions of the AN−1 type of Polychronakos spin chains having long-range interactions. Applying the ‘freezing trick’, here we derive the partition functions for a class of BCN type of Polychronakos spin chains containing supersymmetric analogues of polarized spin reversal operators and subsequently use those partition functions to obtain novel multivariate super Rogers–Szegö (SRS) polynomials depending on four types of variables. We construct the generating functions for such SRS polynomials and show that these polynomials can be written as some bilinear combinations of the AN−1 type of SRS polynomials. We also use the above mentioned generating functions to derive a set of recursion relations for the partition functions of the BCN type of Polychronakos spin chains involving different numbers of lattice sites and internal degrees of freedom.