15 papers
Cherednik integrable system: eigenfunctions at generic eigenvalues
A. Mironov, A. Morozov, A. Popolitov
Symmetric Macdonald polynomials of variables provide eigenfunctions of the -body trigonometric Ruijsenaars-Schneider integrable system at particular eigenvalues. In order to…
Generating twisted Cherednik eigenfunctions
A. Mironov, A. Morozov, A. Popolitov
Hamiltonians of new integrable systems associated with the integer rays (commutative subalgebras) of Ding-Iohara-Miki (DIM) algebra in the -body represe…
Twisted Cherednik spectrum as a -deformation
A. Mironov, A. Morozov, A. Popolitov
The common eigenfunctions of the twisted Cherednik operators can be first analyzed in the limit of . Then, the polynomial eigenfunctions form a simple set origi…
Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems
A. Mironov, A. Morozov, A. Popolitov
We discuss interrelations between eigenfunctions of the Hamiltonians associated with the commutative (integer ray) subalgebras of the Ding-Iohara-Miki algebra and those of the twis…
Nested ansatz method for Baker-Akhiezer functions
A. Mironov, A. Morozov, A. Popolitov
We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for…
Twisted Cherednik systems and non-symmetric Macdonald polynomials
A. Mironov, A. Morozov, A. Popolitov
We consider eigenfunctions of many-body system Hamiltonians associated with generalized (a-twisted) Cherednik operators used in construction of other Hamiltonians: those arising fr…