Polynomials Associated with Dihedral Groups

There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of t...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2007
1. Verfasser: Dunkl, C.F.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2007
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147808
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Polynomials Associated with Dihedral Groups / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 10 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Dunkl, C.F.
author_facet Dunkl, C.F.
citation_txt Polynomials Associated with Dihedral Groups / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 10 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The last section of the paper deals with parameter values for which the formulae have singularities.
first_indexed 2025-11-24T16:26:16Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-11-24T16:26:16Z
publishDate 2007
publisher Інститут математики НАН України
record_format dspace
spelling Dunkl, C.F.
2019-02-16T08:35:28Z
2019-02-16T08:35:28Z
2007
Polynomials Associated with Dihedral Groups / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 10 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 33C45; 33C80; 20F55
https://nasplib.isofts.kiev.ua/handle/123456789/147808
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The last section of the paper deals with parameter values for which the formulae have singularities.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Polynomials Associated with Dihedral Groups
Article
published earlier
spellingShingle Polynomials Associated with Dihedral Groups
Dunkl, C.F.
title Polynomials Associated with Dihedral Groups
title_full Polynomials Associated with Dihedral Groups
title_fullStr Polynomials Associated with Dihedral Groups
title_full_unstemmed Polynomials Associated with Dihedral Groups
title_short Polynomials Associated with Dihedral Groups
title_sort polynomials associated with dihedral groups
url https://nasplib.isofts.kiev.ua/handle/123456789/147808
work_keys_str_mv AT dunklcf polynomialsassociatedwithdihedralgroups