BourbakiV1, Main, Exploration, bibRecord, 000539

On discretization of tori of compact simple Lie groups

Identifieur interne : 000539 ( Main/Exploration ); précédent : 000538; suivant : 000540

On discretization of tori of compact simple Lie groups

Auteurs : Ji Hrivnk [Canada, République tchèque] ; Ji Patera [Canada, République tchèque]

Source :

Journal of Physics A: Mathematical and Theoretical [ 1751-8113 ] ; 2009.

RBID : ISTEX:7CE5D53E4BCACF374A5C5F95542C797425F4649C

English descriptors

KwdEn :
- Adjacent edges, Algebra, Complex semisimple, Conjugacy, Conjugacy classes, Cosets, Cosets representants, Coxeter, Coxeter number, Discrete orthogonality, Dual marks, Dual weight lattice, Explicit formulas, Full generality, Fundamental domain, Fundamental region, Grid, Highest root, Hrivn, Interpolating functions, Interpolation, Invariance, Lattice, Math, Matrix, Maximal torus, Nite, Nite order, Nite series, Node, Orbit functions, Orthogonal, Orthogonal polynomials, Orthogonality, Patera, Phys, Representative element, Root lattice, Semisimple, Simple roots, Squared length, Stabw, Subgraph, Such cosets, Theor, Torus, Weight lattice, Weyl, Weyl group, Weyl groups.
Teeft :
- Adjacent edges, Algebra, Complex semisimple, Conjugacy, Conjugacy classes, Cosets, Cosets representants, Coxeter, Coxeter number, Discrete orthogonality, Dual marks, Dual weight lattice, Explicit formulas, Full generality, Fundamental domain, Fundamental region, Grid, Highest root, Hrivn, Interpolating functions, Interpolation, Invariance, Lattice, Math, Matrix, Maximal torus, Nite, Nite order, Nite series, Node, Orbit functions, Orthogonal, Orthogonal polynomials, Orthogonality, Patera, Phys, Representative element, Root lattice, Semisimple, Simple roots, Squared length, Stabw, Subgraph, Such cosets, Theor, Torus, Weight lattice, Weyl, Weyl group, Weyl groups.

Abstract

Three types of numerical data are provided for simple Lie groups of any type and rank. These data are indispensable for Fourier-like expansions of multidimensional digital data into finite series of C- or S-functions on the fundamental domain F of the underlying Lie group G. Firstly, we determine the number FM of points in F from the lattice PM, which is the refinement of the dual weight lattice P of G by a positive integer M. Secondly, we find the lowest set M of dominant weights, specifying the maximal set of C- and S-functions that are pairwise orthogonal on the point set FM. Finally, we describe an efficient algorithm for finding, on the maximal torus of G, the number of conjugate points to every point of FM. Discrete C- and S-transforms, together with their continuous interpolations, are presented in full generality.

Url:

https://api.istex.fr/document/7CE5D53E4BCACF374A5C5F95542C797425F4649C/fulltext/pdf

DOI: 10.1088/1751-8113/42/38/385208

Affiliations:

Canada, République tchèque

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to stream Main, to step Curation: 000539

Le document en format XML

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On discretization of tori of compact simple Lie groups

On discretization of tori of compact simple Lie groups

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English descriptors

Abstract

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