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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.06784 |
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| _version_ | 1866912884752121856 |
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| author | van Horssen, Max van Pruijssen, Maarten |
| author_facet | van Horssen, Max van Pruijssen, Maarten |
| contents | We give an algebraic construction of shift operators for the non-symmetric Heckman-Opdam polynomials and the non-symmetric Macdonald-Koornwinder polynomials. To each linear character of the finite Weyl group, we associate forward and backward shift operators, which are differential-reflection and difference-reflection operators that satisfy certain transmutation relations with the (Dunkl-)Cherednik operators. In the Heckman-Opdam case, the construction recovers the non-symmetric shift operators of Opdam and Toledano Laredo for the sign character. Furthermore, in rank one, we recover the rank-one non-symmetric shift operators previously obtained by the authors and Schlösser. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06784 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An elementary approach to non-symmetric shift operators and their q-analogs van Horssen, Max van Pruijssen, Maarten Representation Theory Classical Analysis and ODEs 33D80, 33C52, 33D52 We give an algebraic construction of shift operators for the non-symmetric Heckman-Opdam polynomials and the non-symmetric Macdonald-Koornwinder polynomials. To each linear character of the finite Weyl group, we associate forward and backward shift operators, which are differential-reflection and difference-reflection operators that satisfy certain transmutation relations with the (Dunkl-)Cherednik operators. In the Heckman-Opdam case, the construction recovers the non-symmetric shift operators of Opdam and Toledano Laredo for the sign character. Furthermore, in rank one, we recover the rank-one non-symmetric shift operators previously obtained by the authors and Schlösser. |
| title | An elementary approach to non-symmetric shift operators and their q-analogs |
| topic | Representation Theory Classical Analysis and ODEs 33D80, 33C52, 33D52 |
| url | https://arxiv.org/abs/2602.06784 |