Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to gen...
Збережено в:
| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149199 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Цитувати: | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle / M. Đurđevich, S.B. Sontz // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 32 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149199 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1491992019-02-20T01:26:09Z Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle Đurđevich, M. Sontz, S.B. A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero. 2013 Article Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle / M. Đurđevich, S.B. Sontz // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20F55; 81R50; 81R60 DOI: http://dx.doi.org/10.3842/SIGMA.2013.040 http://dspace.nbuv.gov.ua/handle/123456789/149199 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 |
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero. |
| format |
Article |
| author |
Đurđevich, M. Sontz, S.B. |
| spellingShingle |
Đurđevich, M. Sontz, S.B. Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Đurđevich, M. Sontz, S.B. |
| author_sort |
Đurđevich, M. |
| title |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_short |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_full |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_fullStr |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_full_unstemmed |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_sort |
dunkl operators as covariant derivatives in a quantum principal bundle |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149199 |
| citation_txt |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle / M. Đurđevich, S.B. Sontz // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 32 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT đurđevichm dunkloperatorsascovariantderivativesinaquantumprincipalbundle AT sontzsb dunkloperatorsascovariantderivativesinaquantumprincipalbundle |
| first_indexed |
2023-05-20T17:32:13Z |
| last_indexed |
2023-05-20T17:32:13Z |
| _version_ |
1796153529508823040 |