Vector Polynomials and a Matrix Weight Associated to Dihedral Groups
The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case for even dihedral groups). The matrix weight function for th...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146691 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727985221599232 |
|---|---|
| author | Dunkl, C.F. |
| author_facet | Dunkl, C.F. |
| citation_txt | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case for even dihedral groups). The matrix weight function for the Gaussian form is found explicitly by solving a boundary value problem, and then computing the normalizing constant. An orthogonal basis for the homogeneous harmonic polynomials is constructed. The coefficients of these polynomials are found to be balanced terminating ₄F₃-series.
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| first_indexed | 2025-12-07T19:06:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146691 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:06:19Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dunkl, C.F. 2019-02-10T18:58:49Z 2019-02-10T18:58:49Z 2014 Vector Polynomials and a Matrix Weight Associated to Dihedral Groups / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 5 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C52; 20F55; 33C45 DOI:10.3842/SIGMA.2014.044 https://nasplib.isofts.kiev.ua/handle/123456789/146691 The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case for even dihedral groups). The matrix weight function for the Gaussian form is found explicitly by solving a boundary value problem, and then computing the normalizing constant. An orthogonal basis for the homogeneous harmonic polynomials is constructed. The coefficients of these polynomials are found to be balanced terminating ₄F₃-series. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Vector Polynomials and a Matrix Weight Associated to Dihedral Groups Article published earlier |
| spellingShingle | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups Dunkl, C.F. |
| title | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups |
| title_full | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups |
| title_fullStr | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups |
| title_full_unstemmed | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups |
| title_short | Vector Polynomials and a Matrix Weight Associated to Dihedral Groups |
| title_sort | vector polynomials and a matrix weight associated to dihedral groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146691 |
| work_keys_str_mv | AT dunklcf vectorpolynomialsandamatrixweightassociatedtodihedralgroups |