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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0370-2693 |