English

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

Representation Theory 2019-08-06 v2 Mathematical Physics math.MP

Abstract

Coefficients of super Jacobi polynomials of type B(1,n)B(1,n) are rational functions in three parameters k,p,qk,p,q. At the point (1,0,0)(-1,0,0) these coefficient may have poles. Let us set q=0q=0 and consider pair (k,p)(k,p) as a point of A2\Bbb A^2. If we apply blow up procedure at the point (1,0)(-1,0) then we get a new family of polynomials depending on parameter tPt\in \Bbb P. If t=t=\infty then we get supercharacters of Kac modules for Lie supergroup OSP(2,2n)OSP(2,2n) and supercharacters of irreducible modules can be obtained for nonnegative integer tt depending on highest weight. Besides we obtained supercharcters of projective covers as specialisation of some nonsingular modification of super Jacobi polynomials.

Keywords

Cite

@article{arxiv.1906.09753,
  title  = {Supergroup $OSP(2,2n)$ and super Jacobi polynomials},
  author = {G. S. Movsisyan and A. N. Sergeev},
  journal= {arXiv preprint arXiv:1906.09753},
  year   = {2019}
}

Comments

19 pages, extended version

R2 v1 2026-06-23T10:01:29.438Z