Supergroup OSP(2,2n) and super Jacobi polynomials

Abstract

The coefficients of the super Jacobi polynomials of BC1,n-type are rational functions in three parameters k,p,q. At the point (−1,0,0) these coefficients may have poles. Let us set q=0 and consider a pair (k,p) as the point of A2. If we apply blow up procedure at the point (−1,0) then we get a new family of polynomials. This family depends on one parameter t∈P. If t=∞ then we get Euler supercharacters for Lie supergroup OSP(2,2n). The supercharacters of finite dimensional irreducible modules can be also obtained by a specialization of the parameter t. But in such a case the specialization depends on the highest weight of the corresponding irreducible module.