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

Abstract

Coefficients of super Jacobi polynomials of type B(1, n) are rational functions in three parameters k, p, q. At the point (−1, 0, 0) these coefficient may have poles. Let us set q = 0 and consider pair (k, p) as a point of A 2 . If we apply blow up procedure at the point (−1, 0) then we get a new family of polynomials depending on parameter t ∈ P. If t = ∞ then we get supercharacters of Kac modules for Lie supergroup OSP (2, 2n) and supercharacters of irreducible modules can be obtained for nonnegative integer t depending on highest weight. Besides we obtained supercharcters of projective covers as specialisation of some nonsingular modification of super Jacobi polynomials.