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4 papers
Strictly nilpotent elements and bispectral operators in the Weyl algebra
Emil Horozov
In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators wi…
Fuchsian bispectral operators
E. Horozov, T. Milanov
The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in sever…
The Pfaff lattice and skew-orthogonal polynomials
M. Adler, E. Horozov, P. van Moerbeke
Consider a semi-infinite skew-symmetric moment matrix, $m_{\iy}$ evolving according to the vector fields $\pl m / \pl t_k=\Lb^k m+m \Lb^{\top k} ,$ where $\Lb$ is the shift matrix.…
Darboux Transformations of Bispectral Quantum Integrable Systems
Emil Horozov, Alex Kasman
We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differen…