منابع مشابه
BGG sequences on spheres
BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called K-types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing...
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To do homological algebra with unbounded chain complexes one needs to first find a way of constructing resolutions. Spaltenstein solved this problem for chain complexes of R-modules by truncating further and further to the left, resolving the pieces, and gluing back the partial resolutions. Our aim is to give a homotopy theoretical interpretation of this procedure, which may be extended to a re...
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We present a general setup in which one can define an algebra with a regular triangular decomposition. This setup incorporates several important examples in representation theory, including semisimple, Kac-Moody, contragredient, and Borcherds Lie algebras, the Virasoro algebra, and quantum groups. In all these cases, the “Cartan” subalgebra is a commutative cocommutative Hopf algebra; we show t...
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BGG–sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we show that under appropriate torsion freeness and/or semi–flatness assumptions c...
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A non-commutative version of the Bernštĕın-GelfandGelfand (BGG) correspondence is set up, and a sample application is given to periodic injective resolutions. 0. Introduction The Bernštĕın-Gelfand-Gelfand correspondence is surprising. It gives an equivalence of categories gr(E) ≃ D(coh P). This was proved in [4, thm. 2] and as always, to explain such a formula requires lots of words. On the lef...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2016.06.007