The Smallest Singular Values and Vector-Valued Jack Polynomials
There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for the smallest singular values are constructed in terms of the Jack polynomials. The smallest singular values bound the region of positivity of...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209842 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Smallest Singular Values and Vector-Valued Jack Polynomials / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862581797544525824 |
|---|---|
| author | Dunkl, C.F. |
| author_facet | Dunkl, C.F. |
| citation_txt | The Smallest Singular Values and Vector-Valued Jack Polynomials / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for the smallest singular values are constructed in terms of the Jack polynomials. The smallest singular values bound the region of positivity of the bilinear symmetric form for which the Jack polynomials are mutually orthogonal. As background, there are some results about general finite reflection groups and singular values in the context of standard modules of the rational Cherednik algebra.
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| first_indexed | 2025-12-06T17:14:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209842 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-06T17:14:08Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dunkl, C.F. 2025-11-27T14:48:50Z 2018 The Smallest Singular Values and Vector-Valued Jack Polynomials / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C52; 20F55; 05E35; 05E10 arXiv: 1804.09158 https://nasplib.isofts.kiev.ua/handle/123456789/209842 https://doi.org/10.3842/SIGMA.2018.115 There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for the smallest singular values are constructed in terms of the Jack polynomials. The smallest singular values bound the region of positivity of the bilinear symmetric form for which the Jack polynomials are mutually orthogonal. As background, there are some results about general finite reflection groups and singular values in the context of standard modules of the rational Cherednik algebra. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Smallest Singular Values and Vector-Valued Jack Polynomials Article published earlier |
| spellingShingle | The Smallest Singular Values and Vector-Valued Jack Polynomials Dunkl, C.F. |
| title | The Smallest Singular Values and Vector-Valued Jack Polynomials |
| title_full | The Smallest Singular Values and Vector-Valued Jack Polynomials |
| title_fullStr | The Smallest Singular Values and Vector-Valued Jack Polynomials |
| title_full_unstemmed | The Smallest Singular Values and Vector-Valued Jack Polynomials |
| title_short | The Smallest Singular Values and Vector-Valued Jack Polynomials |
| title_sort | smallest singular values and vector-valued jack polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209842 |
| work_keys_str_mv | AT dunklcf thesmallestsingularvaluesandvectorvaluedjackpolynomials AT dunklcf smallestsingularvaluesandvectorvaluedjackpolynomials |