Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras

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• 作者：Shun-Jen Cheng^a ; ¹ ; ^{chengsj@math.sinica.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Jae-Hoon Kwon^b ; ² ; ^{jaehoonkw@snu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Ortho-symplectic Lie superalgebras ; Kac&ndash ; Wakimoto formula
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：1296-1329
• 全文大小：651 K

文摘

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.