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Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II
This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R². The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard...
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Інститут математики НАН України
2013
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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irk-123456789-1492002019-02-20T01:26:03Z Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II Dunkl, C.F. This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R². The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard module of the rational Cherednik algebra for the group W(B₂) (symmetry group of the square) associated to the (2-dimensional) reflection representation. The algebra has two parameters: k₀, k₁. In the previous paper K is determined up to a scalar, namely, the normalization constant. The conjecture stated there is proven in this note. An asymptotic formula for a sum of ₃F₂-type is derived and used for the proof. 2013 Article Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 1 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C52; 33C20 DOI: http://dx.doi.org/10.3842/SIGMA.2013.043 http://dspace.nbuv.gov.ua/handle/123456789/149200 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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English |
| description |
This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R². The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard module of the rational Cherednik algebra for the group W(B₂) (symmetry group of the square) associated to the (2-dimensional) reflection representation. The algebra has two parameters: k₀, k₁. In the previous paper K is determined up to a scalar, namely, the normalization constant. The conjecture stated there is proven in this note. An asymptotic formula for a sum of ₃F₂-type is derived and used for the proof. |
| format |
Article |
| author |
Dunkl, C.F. |
| spellingShingle |
Dunkl, C.F. Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Dunkl, C.F. |
| author_sort |
Dunkl, C.F. |
| title |
Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_short |
Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_full |
Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_fullStr |
Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_full_unstemmed |
Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_sort |
vector-valued polynomials and a matrix weight function with b₂-action. ii |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149200 |
| citation_txt |
Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 1 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT dunklcf vectorvaluedpolynomialsandamatrixweightfunctionwithb2actionii |
| first_indexed |
2023-05-20T17:32:13Z |
| last_indexed |
2023-05-20T17:32:13Z |
| _version_ |
1796153529614729216 |