منابع مشابه
The second cohomology of simple SL2-modules
Let G be the simple algebraic group SL2 defined over an algebraically closed field K of characteristic p > 0. In this paper, we compute the second cohomology of all irreducible representations of G.
متن کاملSL2-modules of small homological dimension
Let Vn be the SL2-module of binary forms of degree n and let V = Vn1 ⊕ . . . ⊕ Vnp . We consider the algebra R = O(V )2 of polynomial functions on V invariant under the action of SL2. The measure of the intricacy of these algebras is the length of their chains of syzygies, called homological dimension hdR. Popov gave in 1983 a classi cation of the cases in which hdR ≤ 10 for a single binary for...
متن کاملIrreducible modules for the quantum affine algebra Uq( ̂ sl2) and its Borel subalgebra Uq( ̂ sl2) ≥0
Let Uq(ŝl2) ≥0 denote the Borel subalgebra of the quantum affine algebra Uq(ŝl2). We show that the following hold for any choice of scalars ε0, ε1 from the set {1,−1}. (i) Let V be a finite-dimensional irreducible Uq(ŝl2) -module of type (ε0, ε1). Then the action of Uq(ŝl2) ≥0 on V extends uniquely to an action of Uq(ŝl2) on V . The resulting Uq(ŝl2)-module structure on V is irreducible and of ...
متن کاملBilinear forms on sl2-modules and a hypergeometric identity
In this paper we study properties of a certain bilinear form on finite dimensional sl2(R)-modules, and how these properties behave with respect to tensor products of modules. An attempt to determine the signature of this form leads to an interesting identity for the hypergeometric series 3F2, which is not the Saalschütz identity. This identity also generalises to an identity for k+1Fk, k ∈ N.
متن کاملA GEOMETRIC CATEGORIFICATION OF TENSOR PRODUCTS OF Uq(sl2)-MODULES
We give a purely geometric categorification of tensor products of finite-dimensional simple Uq(sl2)-modules and R-matrices on them. The work is developed in the framework of category of perverse sheaves and the categorification theorems are understood as consequences of Deligne’s theory of weights.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90254-2