A geometric method in the theory of SLn-representations of groups
نویسنده
چکیده
This paper introduces a new method in the study of representations of groups into affine algebraic groups. In this work we focus on the study of SLnrepresentations and postpone the consideration of the theory in full to future papers. Let G be a group and let R be a commutative ring with unity. There is a commutative R-algebra Repn(G), called the universal representation algebra, and the universal representation
منابع مشابه
Monomial 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 کاملClassification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions
Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...
متن کاملThe efficacy of Isotretinoin-loaded solid lipid nanoparticles in comparison to Isotrex® on acne treatment
Topical retinoids are considered as the first line therapy in the treatment of acne vulgaris, but they are associated with cutaneous irritation. In this study, isotretinoin-loaded solid lipid nanoparticles(IT-SLN) were prepared to treat the mild to moderate acne. Also using IT-SLN would minimize IT adverse effects in comparison to commercial product, Isotrex®. This study was conducted to prepar...
متن کاملA representation for some groups, a geometric approach
In the present paper, we are going to use geometric and topological concepts, entities and properties of the integral curves of linear vector fields, and the theory of differential equations, to establish a representation for some groups on $R^{n} (ngeq 1)$. Among other things, we investigate the surjectivity and faithfulness of the representation. At the end, we give some app...
متن کاملCategorical Geometric Skew Howe Duality
We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(sln) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of Uq(sl2) which are related to representations of Uq(sln) by quant...
متن کامل