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...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146691 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146691 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1466912019-02-11T01:25:01Z Vector Polynomials and a Matrix Weight Associated to Dihedral Groups Dunkl, C.F. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146691 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Dunkl, C.F. |
| spellingShingle |
Dunkl, C.F. Vector Polynomials and a Matrix Weight Associated to Dihedral Groups Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Dunkl, C.F. |
| author_sort |
Dunkl, C.F. |
| title |
Vector Polynomials and a Matrix Weight Associated to Dihedral Groups |
| title_short |
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_sort |
vector polynomials and a matrix weight associated to dihedral groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146691 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT dunklcf vectorpolynomialsandamatrixweightassociatedtodihedralgroups |
| first_indexed |
2023-05-20T17:25:25Z |
| last_indexed |
2023-05-20T17:25:25Z |
| _version_ |
1796153262013939712 |