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The rank two Jacobi algebra
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is s…
Meta Algebras and Biorthogonal Rational Functions: The Hahn Case
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated met…
Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampe +1
The computation of the entanglement entropy for inhomogeneous free fermions chains based on q-Racah polynomials is considered. The eigenvalues of the truncated correlation matrix a…
Bethe ansatz diagonalization of the Heun-Racah operator
Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampe +1
The Heun-Racah operator is diagonalized with the help of the modified algebraic Bethe ansatz. This operator is the most general bilinear expression in two generators of the Racah a…
Chern-Simons theory, link invariants and the Askey-Wilson algebra
Nicolas Crampé, Luc Vinet, Meri Zaimi
The occurrence of the Askey-Wilson (AW) algebra in the Chern-Simons (CS) theory and in the Reshetikhin-Turaev (RT) link invariant construction with quantum algebra $U_q(\ma…
Time and band limiting operator and Bethe ansatz
P. -A. Bernard, N. Crampe, L. Vinet
The time and band limiting operator is introduced to optimize the reconstruction of a signal from only a partial part of its spectrum. In the discrete case, this operator commutes…