Large annihilator category O for sl(∞),o(∞),sp(∞)
نویسندگان
چکیده
منابع مشابه
Category O for Quantum Groups
In this paper we study the BGG-categories Oq associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Usin...
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We study the representation theory of the invariant subalgebra of the Weyl algebra under a torus action, which we call a “hypertoric enveloping algebra.” We define an analogue of BGG category O for this algebra, and identify it with a certain category of sheaves on a hypertoric variety. We prove that a regular block of this category is highest weight and Koszul, identify its Koszul dual, comput...
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We compare properties of (the parabolic version of) the BGG category O for semi-simple Lie algebras with those for classical (not necessarily simple) Lie superalgebras.
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Let g be a simple Lie algebra. We consider the category Ô of those modules over the affine quantum group Uq(ĝ) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category Ô. In particular, we develop the theory of q-characters a...
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In this paper we introduce a general axiomatic framework for algebras with triangular decomposition, which allows for a systematic study of the Bernstein-Gelfand-Gelfand Category O. Our axiomatic framework can be stated via three relatively simple axioms, and it encompasses a very large class of algebras studied in the literature. We term the algebras satisfying our axioms as regular triangular...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2019
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.05.020