Dunkl Operators and Canonical Invariants of Reflection Groups
Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral g...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149139 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Dunkl Operators and Canonical Invariants of Reflection Groups / A. Berenstein, Y. Burman // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862662177708572672 |
|---|---|
| author | Berenstein, A. Burman, Y. |
| author_facet | Berenstein, A. Burman, Y. |
| citation_txt | Dunkl Operators and Canonical Invariants of Reflection Groups / A. Berenstein, Y. Burman // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions.
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| first_indexed | 2025-12-02T13:44:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149139 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T13:44:27Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Berenstein, A. Burman, Y. 2019-02-19T17:37:57Z 2019-02-19T17:37:57Z 2009 Dunkl Operators and Canonical Invariants of Reflection Groups / A. Berenstein, Y. Burman // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 20 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 20F55; 15A72 https://nasplib.isofts.kiev.ua/handle/123456789/149139 Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions. This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The work was partially supported by the CRDF grant RUM1-2895-MO-07. The second author was also supported by the INTAS grant 05-7805, RFBR grants 08-01-00110-a and NSh709.2008.1, and the HSE Scientific Foundation grant 08-01-0019. The authors are grateful to P. Etingof, M. Feigin, A. Samokhin, and Y. Xu for valuable discussions. The second author wishes to thank the University of Oregon, where most of this work was carried out, for its warm hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dunkl Operators and Canonical Invariants of Reflection Groups Article published earlier |
| spellingShingle | Dunkl Operators and Canonical Invariants of Reflection Groups Berenstein, A. Burman, Y. |
| title | Dunkl Operators and Canonical Invariants of Reflection Groups |
| title_full | Dunkl Operators and Canonical Invariants of Reflection Groups |
| title_fullStr | Dunkl Operators and Canonical Invariants of Reflection Groups |
| title_full_unstemmed | Dunkl Operators and Canonical Invariants of Reflection Groups |
| title_short | Dunkl Operators and Canonical Invariants of Reflection Groups |
| title_sort | dunkl operators and canonical invariants of reflection groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149139 |
| work_keys_str_mv | AT berensteina dunkloperatorsandcanonicalinvariantsofreflectiongroups AT burmany dunkloperatorsandcanonicalinvariantsofreflectiongroups |