Type C∨C DAHA and Koornwinder systems mirror type-A Macdonald structures for Hamiltonians, recursions, evaluations and dualities, but lack a usable Noumi-Shiraishi-style universal series and SL(2,Z)-type twisting automorphisms.
Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems
1 Pith paper cite this work. Polarity classification is still indexing.
abstract
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 twisted Cherednik system. In the case of $t=q^{-m}$ with natural $m$, eigenfunctions of the first system of Hamiltonians are the twisted Baker-Akhiezer functions (BAFs) introduced by O. Chalykh, while eigenfunctions of the twisted Cherednik Hamiltonians are twisted non-symmetric Macdonald polynomials. Actually, the twisted Cherednik ground state is symmetric and coincides with a peculiar symmetric BAF. We lift this correspondence to excited states, and claim that both Cherednik eigenfunctions and BAF's can be combined to produce symmetric functions, which coincide with each other and are eigenfunctions of the both DIM Hamiltonians and power sums of the twisted Cherednik Hamiltonians at once. This reflects the correspondence between the DIM algebra and the spherical DAHA explicitly.
fields
hep-th 1years
2026 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Integrable systems inspired by DAHA and DIM algebra: type $C^\vee C$ versus type $A$
Type C∨C DAHA and Koornwinder systems mirror type-A Macdonald structures for Hamiltonians, recursions, evaluations and dualities, but lack a usable Noumi-Shiraishi-style universal series and SL(2,Z)-type twisting automorphisms.