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Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
Akinori Nishino, Hideaki Ujino, Miki Wadati
Extending a method developed by Takamura and Takano, we present the Rodrigues formula for the nonsymmetric multivariable Laguerre polynomials which form the orthogonal basis for th…
Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
Hideaki Ujino, Miki Wadati
Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we present the Rodrigues formula for the nonsymmetric multivariable Hermite polynomial.
New Non-Symmetric Orthogonal Basis for the Calogero Model with Distinguishable Particles
Hideaki Ujino, Akinori Nishino, Miki Wadati
We demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved operators for distinguishable particles governed by the Calogero Hamiltonian. Our c…
SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model
Masahiro Shiroishi, Hideaki Ujino, Miki Wadati
The SO(4) invariance of the transfer matrix for the one-dimensional Hubbard model is clarified from the QISM (quantum inverse scattering method) point of view. We demonstrate the S…
The Calogero Model: Integrable Structures and Orthogonal Basis
Miki Wadati, Hideaki Ujino
Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operator…
Orthogonal Symmetric Polynomials Associated with the Calogero Model
Hideaki Ujino
The Calogero model is a one-dimensional quantum integrable system with inverse-square long-range interactions confined in an external harmonic well. It shares the same algebraic st…