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: Berenstein, A., Burman, Y.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
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
id nasplib_isofts_kiev_ua-123456789-149139
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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Dunkl Operators and Canonical Invariants of Reflection Groups
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Dunkl Operators and Canonical Invariants of Reflection Groups
spellingShingle Dunkl Operators and Canonical Invariants of Reflection Groups
Berenstein, A.
Burman, Y.
title_short 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_sort dunkl operators and canonical invariants of reflection groups
author Berenstein, A.
Burman, Y.
author_facet Berenstein, A.
Burman, Y.
publishDate 2009
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149139
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.
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first_indexed 2025-12-02T13:44:27Z
last_indexed 2025-12-02T13:44:27Z
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