A_2l⁽²⁾ at level -l-(1)/(2)

2020/07/31 by Shashank Kanade, Kanade, Shashank
Mathematics · Physics and Astronomy · #17B67 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2008.00108

openalex publication_date 2020/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L_l=L(\mathfraksl_2l+1,-l-(1)/(2)) be the simple vertex operator algebra based on the affine Lie algebra \widehat\mathfraksl_2l+1 at boundary admissible level -l-(1)/(2). We consider a lift ν of the Dynkin diagram involution of A_2l=\mathfraksl_2l+1 to an involution of L_l. The ν-twisted L_l-modules are A_2l⁽²⁾-modules of level -l-(1)/(2) with an anti-homogeneous realization. We classify simple ν-twisted highest-weight (weak) L_l-modules using twisted Zhu algebras and singular vectors for \widehat\mathfraksl_2l+1 at level -l-(1)/(2) obtained by Perše. We find that there are finitely many such modules up to isomorphism, and the ν-twisted (weak) L_l-modules that are in category \mathscrO for A_2l⁽²⁾ are semi-simple.

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