BourbakiV1, France, Analysis, bibRecord, 000392

Polytopes Associated to Demazure Modules of Symmetrizable Kac–Moody Algebras of Rank Two

Identifieur interne : 000392 ( France/Analysis ); précédent : 000391; suivant : 000393

Polytopes Associated to Demazure Modules of Symmetrizable Kac–Moody Algebras of Rank Two

Auteurs : Raika Dehy [France]

Source :

Journal of Algebra [ 0021-8693 ] ; 2000.

RBID : ISTEX:1FD7BA75DEE51C8665B11EDCBB056F431C56D8D8

English descriptors

KwdEn :
- Affine, Algebra, Borel subgroup, Canonical, Canonical basis, Certain demazure modules, Convex, Convex envelope, Convex polytopes, Dehy, Demazure, Demazure module, Demazure modules, Dominant weight, Eigenweight vector, Flat deformation, Fundamental weight, Fundamental weights, Grobner, Grobner basis, Integral coordinates, Integral point, Integral points, Irreducible, Irreducible representation, Isomorphic, Line bundles, Littelmann, Maximal element, Minkowski, Minkowski sums, Module, Monomial, Monomials, Multicone, Nonstandard monomial, Other hand, Other words, Polytope, Polytopes, Previous section, Raika, Raika dehy, Schubert varieties, Schubert variety, Shorter root, Simple roots, Smallest number, Standard monomial theory, Standard monomials, Sym2, Symmetrizable algebras, Toric, Toric variety, Vector space, Weyl, Weyl group, Wty1.
Teeft :
- Affine, Algebra, Borel subgroup, Canonical, Canonical basis, Certain demazure modules, Convex, Convex envelope, Convex polytopes, Dehy, Demazure, Demazure module, Demazure modules, Dominant weight, Eigenweight vector, Flat deformation, Fundamental weight, Fundamental weights, Grobner, Grobner basis, Integral coordinates, Integral point, Integral points, Irreducible, Irreducible representation, Isomorphic, Line bundles, Littelmann, Maximal element, Minkowski, Minkowski sums, Module, Monomial, Monomials, Multicone, Nonstandard monomial, Other hand, Other words, Polytope, Polytopes, Previous section, Raika, Raika dehy, Schubert varieties, Schubert variety, Shorter root, Simple roots, Smallest number, Standard monomial theory, Standard monomials, Sym2, Symmetrizable algebras, Toric, Toric variety, Vector space, Weyl, Weyl group, Wty1.

Abstract

Abstract: Let ω1,ω2 be the two fundamental weights of a symmetrizable Kac–Moody algebra g of rank two (hence necessarily affine or finite), and τ an element of the Weyl group. In this paper we construct polytopes Pτ(ω1),Pτ(ω2)⊂Rl(τ) and a linear map ξ: Rl(τ)→h* such that for any dominant weight λ=k1ω1+k2ω2, we have CharEτ(λ)=eλ∑eξ(x), where the sum is over all the integral points x, of the polytope k1Pτ(ω1)+k2Pτ(ω2). Furthermore, we show that there exists a flat deformation of the Schubert variety Sτ into the toric variety defined by Pτ(ω1),Pτ(ω2).

Url:

https://api.istex.fr/document/1FD7BA75DEE51C8665B11EDCBB056F431C56D8D8/fulltext/pdf

DOI: 10.1006/jabr.1999.8208

Affiliations:

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<front><div type="abstract" xml:lang="en">Abstract: Let ω1,ω2 be the two fundamental weights of a symmetrizable Kac–Moody algebra g of rank two (hence necessarily affine or finite), and τ an element of the Weyl group. In this paper we construct polytopes Pτ(ω1),Pτ(ω2)⊂Rl(τ) and a linear map ξ: Rl(τ)→h* such that for any dominant weight λ=k1ω1+k2ω2, we have CharEτ(λ)=eλ∑eξ(x), where the sum is over all the integral points x, of the polytope k1Pτ(ω1)+k2Pτ(ω2). Furthermore, we show that there exists a flat deformation of the Schubert variety Sτ into the toric variety defined by Pτ(ω1),Pτ(ω2).</div>
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Polytopes Associated to Demazure Modules of Symmetrizable Kac–Moody Algebras of Rank Two

Polytopes Associated to Demazure Modules of Symmetrizable Kac–Moody Algebras of Rank Two

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Abstract

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