On complexes relating the Jacobi-Trudi identity with the Bernstein-Gelfand-Gelfand resolution
نویسندگان
چکیده
منابع مشابه
On the Bernstein-Gelfand-Gelfand resolution for Kac-Moody algebras and quantized enveloping algebras
A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-Gelfand resolution for symmetrizable Kac-Moody algebras are established. For quantized enveloping algebras with fixed deformation parameter q ∈ C \ {0} exactness is proven for all q which are not a root of un...
متن کاملA generalization of the category O of Bernstein–Gelfand–Gelfand
In the study of simple modules over a simple complex Lie algebra, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this note, we define a family of categories which generalizes the BGG category. We classify the simple modules for some of these categories. As a consequence we show that these categories are semisimple....
متن کاملDifferential forms via the Bernstein-Gelfand-Gelfand resolution for quantized irreducible flag manifolds
The quantum group version of the Bernstein-Gelfand-Gelfand resolution is used to construct a double complex of Uq(g)-modules with exact rows and columns. The locally finite dual of its total complex is identified with the de Rham complex for quantized irreducible flag manifolds. MSC: 17B37, 58B32
متن کاملJa n 20 00 BERNSTEIN – GELFAND – GELFAND SEQUENCES
This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P , where G is a real or complex semisimple Lie group and P ⊂ G is a parabolic subgroup. We use methods from differential geometry and very elementary finite–dimensional representation theory to construct sequences of invariant differential operators for such geometries, both in the smooth and the holomor...
متن کاملBernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over Z(p) for representations with p-small weights
Let G be a connected reductive linear algebraic group defined and split over Z, let T be a maximal torus, W the Weyl group, R the root system, R the set of coroots, R a set of positive roots, and ρ the half-sum of the elements of R. Let X = X(T ) be the character group of T and let X be the set of those λ ∈ X such that 〈λ, α〉 ≥ 0 for all α ∈ R. For any λ ∈ X, let VZ(λ) be the Weyl module for G ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90122-6