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Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras

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.

preprint2015arXivOpen access
Shun-Jen ChengJae-Hoon Kwon
math.RT
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Shun-Jen ChengJae-Hoon Kwon

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