On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians
Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at t=q−m to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreo...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-04-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269325001406 |
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| author | A. Mironov A. Morozov A. Popolitov |
| author_facet | A. Mironov A. Morozov A. Popolitov |
| author_sort | A. Mironov |
| collection | DOAJ |
| description | Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at t=q−m to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg Chalykh suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the (−1,a) rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support. |
| format | Article |
| id | doaj-art-399bedb7261a43c5bac752884f8b9f49 |
| institution | DOAJ |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj-art-399bedb7261a43c5bac752884f8b9f492025-08-20T02:50:45ZengElsevierPhysics Letters B0370-26932025-04-0186313938010.1016/j.physletb.2025.139380On Chalykh's approach to eigenfunctions of DIM-induced integrable HamiltoniansA. Mironov0A. Morozov1A. Popolitov2Lebedev Physics Institute, Moscow 119991, Russia; NRC “Kurchatov Institute”, 123182, Moscow, Russia; Institute for Information Transmission Problems, Moscow 127994, Russia; Corresponding author.MIPT, Dolgoprudny, 141701, Russia; NRC “Kurchatov Institute”, 123182, Moscow, Russia; Institute for Information Transmission Problems, Moscow 127994, RussiaMIPT, Dolgoprudny, 141701, Russia; NRC “Kurchatov Institute”, 123182, Moscow, Russia; Institute for Information Transmission Problems, Moscow 127994, RussiaQuite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at t=q−m to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg Chalykh suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the (−1,a) rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support.http://www.sciencedirect.com/science/article/pii/S0370269325001406 |
| spellingShingle | A. Mironov A. Morozov A. Popolitov On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians Physics Letters B |
| title | On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians |
| title_full | On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians |
| title_fullStr | On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians |
| title_full_unstemmed | On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians |
| title_short | On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians |
| title_sort | on chalykh s approach to eigenfunctions of dim induced integrable hamiltonians |
| url | http://www.sciencedirect.com/science/article/pii/S0370269325001406 |
| work_keys_str_mv | AT amironov onchalykhsapproachtoeigenfunctionsofdiminducedintegrablehamiltonians AT amorozov onchalykhsapproachtoeigenfunctionsofdiminducedintegrablehamiltonians AT apopolitov onchalykhsapproachtoeigenfunctionsofdiminducedintegrablehamiltonians |