Embeddings of homogeneous spaces into irreducible modules
نویسندگان
چکیده
منابع مشابه
Embeddings of Homogeneous Spaces into Irreducible Modules
Let G be a connected reductive group. We find a necessary and sufficient condition for a quasiaffine homogeneous space of G/H to be embeddable into an irreducible G-module. If H is reductive we also find a necessary and sufficient condition for a closed embedding of G/H into an irreducible module to exist. These conditions are stated in terms of the group of central automorphisms of G/H .
متن کاملAffine Embeddings of Homogeneous Spaces
Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...
متن کاملEmbeddings of Homogeneous Spaces in Prime Characteristics
Let X be a projective algebraic variety over an algebraically closed field k admitting a homogeneous action of a semisimple linear algebraic group G. Then X can be canonically identified with the homogeneous space G/Gx, where x is a closed point in X and Gx the stabilizer group scheme of x. A group scheme over a field of characteristic 0 is reduced so in this case, X is isomorphic to a generali...
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملEquivariant Embeddings of Trees into Hyperbolic Spaces
For every cardinal α ≥ 2 there are three complete constant curvature model manifolds of Hilbert dimension α: the sphere S, the Euclidean space E and the hyperbolic space H. Studying isometric actions on these spaces corresponds in the first case to studying orthogonal representations and in the second case to studying cohomology in degree one with orthogonal representations as coefficients. In ...
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: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.07.022