Super-Hamiltonians for super-Macdonald polynomials
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909596430368768 |
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| author | Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita |
| author_facet | Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita |
| contents | The Macdonald finite-difference Hamiltonian is lifted to a super-generalization. In addition to canonical bosonic time variables $p_k$ new Grassmann time variables $θ_k$ are introduced, and the Hamiltonian is represented as a differential operator acting on a space of functions of both types of variables $p_k$ and $θ_k$. Eigenfunctions for this Hamiltonian are a suitable generalization of Macdonald polynomials to super-Macdonald polynomials discussed earlier in the literature. Peculiarities of the construction in comparison to the canonical bosonic case are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Super-Hamiltonians for super-Macdonald polynomials Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory The Macdonald finite-difference Hamiltonian is lifted to a super-generalization. In addition to canonical bosonic time variables $p_k$ new Grassmann time variables $θ_k$ are introduced, and the Hamiltonian is represented as a differential operator acting on a space of functions of both types of variables $p_k$ and $θ_k$. Eigenfunctions for this Hamiltonian are a suitable generalization of Macdonald polynomials to super-Macdonald polynomials discussed earlier in the literature. Peculiarities of the construction in comparison to the canonical bosonic case are discussed. |
| title | Super-Hamiltonians for super-Macdonald polynomials |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2501.14714 |