Higher Order Deformed Elliptic Ruijsenaars Operators

@article{Hallns2022HigherOD,
  title={Higher Order Deformed Elliptic Ruijsenaars Operators},
  author={Martin A. Halln{\"a}s and Edwin Langmann and Masatoshi Noumi and Hjalmar Rosengren},
  journal={Communications in Mathematical Physics},
  year={2022}
}
We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was previously introduced by Feigin and Silantyev. They provide a quantum mechanical description of two kinds of relativistic quantum mechanical particles which can be identified with particles and anti-particles in an underlying quantum field theory. We give direct proofs of the commutativity of our operators… 
Wall-crossing for vortex partition function and handsaw quiver varierty
. We investigate vortex partition functions defined from integrals over the handsaw quiver varieties of type A 1 via wall-crossing phenomena. We consider vortex partition functions defined by two types
From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators
Kajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with A-type root systems of different ranks. By specialisations of his

References

SHOWING 1-10 OF 30 REFERENCES
From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators
Kajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with A-type root systems of different ranks. By specialisations of his
Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed
Duality in elliptic Ruijsenaars system and elliptic symmetric functions
We demonstrate that the symmetric elliptic polynomials $$E_\lambda (x)$$ E λ ( x ) originally discovered in the study of generalized Noumi–Shiraishi functions are eigenfunctions of
An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A
We introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type A. These operators are related to Ruijsenaars’
Ruijsenaars’ commuting difference operators and invariant subspace spanned by theta functions
We study a family of mutually commutative difference operators introduced by Ruijsenaars. The conjugations of these operators with an appropriate function give the Hamiltonians of some relativistic
Solution of the One‐Dimensional N‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
The quantum‐mechanical problems of N 1‐dimensional equal particles of mass m interacting pairwise via quadratic (``harmonical'') and/or inversely quadratic (``centrifugal'') potentials is solved. In
Veselov New integrable generalizations of Calogero-Moser quantum problem
A one-parameter deformation of Calogero–Moser quantum problem is introduced. It is shown that corresponding Schrodinger operator is integrable for any value of the parameter and algebraically
...
...