Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)
| Autor: | Boe, Brian D., Kujawa, Jonathan R., Nakano, Daniel K. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Compositio Math. 148 (2012) 1561-1592 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/S0010437X12000231 |
| Popis: | Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module. Comment: 32 pages |
| Databáze: | arXiv |
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