Classification of Simple Strong Harish-Chandra Modules Over the Lie Superalgebra of Vector Fields on $\mathbb {C}^{m|n}$

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2025年4月30日

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Yan-an Cai,
Rencai Lü,
Yaohui Xue

摘要

In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra $W_{m,n}$ $W_{m, n}$ of vector fields on $\mathbb {C}^{m|n}$ $C^{m | n}$ . Any such module is the unique simple submodule of some tensor module F(P, V) for a simple weight module P over the Weyl superalgebra $\mathcal {K}_{m,n}$ $K_{m, n}$ and a simple weight module V over the general linear superalgebra $\mathfrak {gl}_{m,n}$ ${gl}_{m, n}$ .

Classification of Simple Strong Harish-Chandra Modules Over the Lie Superalgebra of Vector Fields on \(\mathbb {C}^{m|n}\)

摘要