As is well known, multivariate Rogers-Szegö polynomials are closely connected with the partition functions of the A_N-1 type of Polychronakos spin chains having long-range interactions. Applying the 'freezing trick', here we derive the partition functions for a class of BC_N 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

more »

... nding 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 A_N-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 BC_N type of Polychronakos spin chains involving different numbers of lattice sites and internal degrees of freedom.