On generalized Macdonald polynomials
Abstract Generalized Macdonald polynomials (GMP) are eigenfunctions of specificallydeformed Ruijsenaars Hamiltonians and are built as triangular polylinear combinations of Macdonald polynomials. They are orthogonal with respect to a modified scalar product, which could be constructed with the help...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2020)110 |
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| Summary: | Abstract Generalized Macdonald polynomials (GMP) are eigenfunctions of specificallydeformed Ruijsenaars Hamiltonians and are built as triangular polylinear combinations of Macdonald polynomials. They are orthogonal with respect to a modified scalar product, which could be constructed with the help of an increasingly important triangular perturbation theory, showing up in a variety of applications. A peculiar feature of GMP is that denominators in this expansion are fully factorized, which is a consequence of a hidden symmetry resulting from the special choice of the Hamiltonian deformation. We introduce also a simplified but deformed version of GMP, which we call generalized Schur functions. Our basic examples are bilinear in Macdonald polynomials. |
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| ISSN: | 1029-8479 |