On E-discretization of tori of compact simple Lie groups
Identifieur interne : 000397 ( Main/Exploration ); précédent : 000396; suivant : 000398On E-discretization of tori of compact simple Lie groups
Auteurs : Ji Hrivnk [Canada, République tchèque] ; Ji Patera [Canada]Source :
- Journal of Physics A: Mathematical and Theoretical [ 1751-8113 ] ; 2010.
English descriptors
- KwdEn :
- Algebra, Congruence number, Coset representants, Coxeter number, Discrete orthogonality, Disjoint, Fundamental domain, Fundamental region, Grid, Hrivn, Interpolating functions, Lattice, Math, Nite, Orbit functions, Orthogonal, Orthogonality, Patera, Phys, Root lattice, Semidirect product, Simple roots, Stabilizer, Stabilizer stabw, Stabw, Stabweaff, Subgroup, Theor, Unique shift, Weaff, Weyl, Weyl group, Weyl groups.
- Teeft :
- Algebra, Congruence number, Coset representants, Coxeter number, Discrete orthogonality, Disjoint, Fundamental domain, Fundamental region, Grid, Hrivn, Interpolating functions, Lattice, Math, Nite, Orbit functions, Orthogonal, Orthogonality, Patera, Phys, Root lattice, Semidirect product, Simple roots, Stabilizer, Stabilizer stabw, Stabw, Stabweaff, Subgroup, Theor, Unique shift, Weaff, Weyl, Weyl group, Weyl groups.
Abstract
Three types of numerical data are provided for compact simple Lie groups G of classical types and of any rank. These data are indispensable for Fourier-like expansions of multidimensional digital data into finite series of E-functions on the fundamental domain Fe. Firstly, we determine the number FeM of points in Fe 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 eM of the weights, specifying the maximal set of E-functions that are pairwise orthogonal on the point set FeM. Finally, we describe an efficient algorithm for finding the number of conjugate points to every point of FeM. Discrete E-transform, together with its continuous interpolation, is presented in full generality.
Url:
DOI: 10.1088/1751-8113/43/16/165206
Affiliations:
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Phys. A: Math. Theor.</title><idno type="ISSN">1751-8113</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2010">2010</date><biblScope unit="volume">43</biblScope><biblScope unit="issue">16</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="16">16</biblScope><biblScope unit="production">Printed in the UK & the USA</biblScope></imprint><idno type="ISSN">1751-8113</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1751-8113</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algebra</term><term>Congruence number</term><term>Coset representants</term><term>Coxeter number</term><term>Discrete orthogonality</term><term>Disjoint</term><term>Fundamental domain</term><term>Fundamental region</term><term>Grid</term><term>Hrivn</term><term>Interpolating functions</term><term>Lattice</term><term>Math</term><term>Nite</term><term>Orbit functions</term><term>Orthogonal</term><term>Orthogonality</term><term>Patera</term><term>Phys</term><term>Root lattice</term><term>Semidirect product</term><term>Simple roots</term><term>Stabilizer</term><term>Stabilizer stabw</term><term>Stabw</term><term>Stabweaff</term><term>Subgroup</term><term>Theor</term><term>Unique shift</term><term>Weaff</term><term>Weyl</term><term>Weyl group</term><term>Weyl groups</term></keywords><keywords scheme="Teeft" xml:lang="en"><term>Algebra</term><term>Congruence number</term><term>Coset representants</term><term>Coxeter number</term><term>Discrete orthogonality</term><term>Disjoint</term><term>Fundamental domain</term><term>Fundamental region</term><term>Grid</term><term>Hrivn</term><term>Interpolating functions</term><term>Lattice</term><term>Math</term><term>Nite</term><term>Orbit functions</term><term>Orthogonal</term><term>Orthogonality</term><term>Patera</term><term>Phys</term><term>Root lattice</term><term>Semidirect product</term><term>Simple roots</term><term>Stabilizer</term><term>Stabilizer stabw</term><term>Stabw</term><term>Stabweaff</term><term>Subgroup</term><term>Theor</term><term>Unique shift</term><term>Weaff</term><term>Weyl</term><term>Weyl group</term><term>Weyl groups</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">Three types of numerical data are provided for compact simple Lie groups G of classical types and of any rank. These data are indispensable for Fourier-like expansions of multidimensional digital data into finite series of E-functions on the fundamental domain Fe. Firstly, we determine the number FeM of points in Fe 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 eM of the weights, specifying the maximal set of E-functions that are pairwise orthogonal on the point set FeM. Finally, we describe an efficient algorithm for finding the number of conjugate points to every point of FeM. Discrete E-transform, together with its continuous interpolation, is presented in full generality.</div></front></TEI><affiliations><list><country><li>Canada</li><li>République tchèque</li></country></list><tree><country name="Canada"><noRegion><name sortKey="Hrivnk, Ji" sort="Hrivnk, Ji" uniqKey="Hrivnk J" first="Ji" last="Hrivnk">Ji Hrivnk</name></noRegion><name sortKey="Patera, Ji" sort="Patera, Ji" uniqKey="Patera J" first="Ji" last="Patera">Ji Patera</name><name sortKey="Patera, Ji" sort="Patera, Ji" uniqKey="Patera J" first="Ji" last="Patera">Ji Patera</name></country><country name="République tchèque"><noRegion><name sortKey="Hrivnk, Ji" sort="Hrivnk, Ji" uniqKey="Hrivnk J" first="Ji" last="Hrivnk">Ji Hrivnk</name></noRegion><name sortKey="Hrivnk, Ji" sort="Hrivnk, Ji" uniqKey="Hrivnk J" first="Ji" last="Hrivnk">Ji Hrivnk</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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