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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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-03-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/052/ |
| _version_ | 1828879608367284224 |
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| author | Charles F. Dunkl |
| author_facet | Charles F. Dunkl |
| author_sort | Charles F. Dunkl |
| collection | DOAJ |
| 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 | 2024-12-13T09:31:35Z |
| format | Article |
| id | doaj.art-84ac8cfea6ee49b099fd80b8899b49df |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-13T09:31:35Z |
| publishDate | 2007-03-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-84ac8cfea6ee49b099fd80b8899b49df2022-12-21T23:52:29ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-03-013052Polynomials Associated with Dihedral GroupsCharles F. DunklThere 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.http://www.emis.de/journals/SIGMA/2007/052/intertwining operatorJacobi polynomials |
| spellingShingle | Charles F. Dunkl Polynomials Associated with Dihedral Groups Symmetry, Integrability and Geometry: Methods and Applications intertwining operator Jacobi polynomials |
| 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 |
| topic | intertwining operator Jacobi polynomials |
| url | http://www.emis.de/journals/SIGMA/2007/052/ |
| work_keys_str_mv | AT charlesfdunkl polynomialsassociatedwithdihedralgroups |