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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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)110 |
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| author | A. Mironov A. Morozov |
| author_facet | A. Mironov A. Morozov |
| author_sort | A. Mironov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8bed2b1f9c9f44d0873ea7e6bd6fbcbd |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-8bed2b1f9c9f44d0873ea7e6bd6fbcbd2025-01-26T12:11:42ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020113310.1007/JHEP01(2020)110On generalized Macdonald polynomialsA. Mironov0A. Morozov1I.E. Tamm Theory Department, Lebedev Physics InstituteMoscow Institute of Physics and TechnologyAbstract 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.https://doi.org/10.1007/JHEP01(2020)110Conformal and W SymmetryIntegrable HierarchiesQuantum Groups |
| spellingShingle | A. Mironov A. Morozov On generalized Macdonald polynomials Journal of High Energy Physics Conformal and W Symmetry Integrable Hierarchies Quantum Groups |
| title | On generalized Macdonald polynomials |
| title_full | On generalized Macdonald polynomials |
| title_fullStr | On generalized Macdonald polynomials |
| title_full_unstemmed | On generalized Macdonald polynomials |
| title_short | On generalized Macdonald polynomials |
| title_sort | on generalized macdonald polynomials |
| topic | Conformal and W Symmetry Integrable Hierarchies Quantum Groups |
| url | https://doi.org/10.1007/JHEP01(2020)110 |
| work_keys_str_mv | AT amironov ongeneralizedmacdonaldpolynomials AT amorozov ongeneralizedmacdonaldpolynomials |