Abstract
Let g be a restricted Lie superalgebra of Cartan type W(n), S(n)or H(n) over an algebraically closed field k of prime characteristic p > 3, in the sense of modular version of Kac’s definition in 1977. In this note, we show that the restricted representation category over g has only one block (reckoning parities in). This phenomenon is very different from the case of characteristic zero.
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We thank the referees for their helpful comments.
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This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11601116, 11671138 and 11771279), Shanghai Key Laboratory of PMMP (Grant No. 13dz2260400), the Scientific Research Foundation of Hebei Education Department (Grant No. QN2017090) and the Doctoral Foundation of Hebei Normal University (Grant No. L2016B02)
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Duan, F.F., Shu, B. & Yao, Y.F. On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type. Acta. Math. Sin.-English Ser. 36, 1061–1075 (2020). https://doi.org/10.1007/s10114-020-9469-z
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DOI: https://doi.org/10.1007/s10114-020-9469-z