2013/09/06 by Yuezhu Wu, Wu, Yuezhu, R. B. Zhang +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1309.1533
openalex publication_date 2013/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not A(m,n) (m≠ n) or C(m). Here we treat the latter affine superalgebras to complete the classification. The problem boils down to classifying the irreducible zero-level integrable modules with finite dimensional weight spaces for these affine superalgebras, which is solved in this paper. We note in particular that such modules for A(m,n) (m≠ n) and C(m) must be of highest weight type, but are not necessarily loop modules. This is in sharp contrast to the cases of ordinary affine algebras and the other types of affine superalgebras.