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This article is cited in 19 scientific papers (total in 19 papers)
Category of $\mathfrak{sp}(2n)$-modules with bounded weight multiplicities
D. Grantcharova, V. V. Serganovab a Department of Computer Science San Jose State University
b University of California, Berkeley
Abstract:
Let $\mathfrak g$ be a finite dimensional simple Lie algebra. Denote by $\mathcal B$ the category of all bounded weight $\mathfrak g$-modules, i.e. those which are direct sum of their weight spaces and have uniformly bounded weight multiplicities. A result of Fernando shows that infinite-dimensional bounded weight modules exist only for $\mathfrak g=\mathfrak{sl}(n)$ and $\mathfrak g=\mathfrak{sp}(2n)$. If $\mathfrak g =\mathfrak{sp}(2n)$ we show that $\mathcal B$ has enough projectives if and only if $n>1$. In addition, the indecomposable projective modules can be parameterized and described explicitly. All indecomposable objects are described in terms of indecomposable representations of a certain quiver with relations. This quiver is wild for $n>2$. For $n=2$ we describe all indecomposables by relating the blocks of $\mathcal B$ to the representations of the affine quiver $A_3^{(1)}$.
Key words and phrases:
Lie algebra, indecomposable representations, quiver, weight modules.
Received: December 1, 2005
Citation:
D. Grantcharov, V. V. Serganova, “Category of $\mathfrak{sp}(2n)$-modules with bounded weight multiplicities”, Mosc. Math. J., 6:1 (2006), 119–134
Linking options:
https://www.mathnet.ru/eng/mmj239 https://www.mathnet.ru/eng/mmj/v6/i1/p119
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Abstract page: | 273 | References: | 56 |
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