Shun-Jen Cheng, Jae-Hoon Kwon
Published 2014-06-26, updated 2015-11-10Version 3
We classify finite-dimensional tame modules over the ortho-symplectic Lie superalgebras. For these modules we show that their characters are given by the Kac-Wakimoto character formula, thus establishing the Kac-Wakimoto conjecture for the ortho-symplectic Lie superalgebras. We further relate the Kac-Wakimoto formula to the super Jacobi polynomials of Sergeev and Veselov, and show that these polynomials, up to a sign, give the super characters for these tame modules.
Character Formulae for Ortho-symplectic Lie Superalgebras $\mathfrak{osp}(n|2)$
Super duality and irreducible characters of ortho-symplectic Lie superalgebras
Remarks on modules of the ortho-symplectic Lie superalgebras
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