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On generalized Macdonald polynomials
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Generalized Macdonald polynomials (GMP) are eigenfunctions of specifically-deformed Ruijsenaars Hamiltonians and are built as triangular polylinear combinations of Macdonald polynomials. They are orthogonal with respect to a modified scalar product, which could be constructed with the help of an increasingly important triangular perturbation theory, showing up in a variety of applications. A peculiar feature of GMP is that denominators in this expansion are fully factorized, which is a consequence of a hidden symmetry resulting from the special choice of the Hamiltonian deformation. We introduce also a simplified but deformed version of GMP, which we call generalized Schur functions. Our basic examples are bilinear in Macdonald polynomials.
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Cited by 1 Pith paper
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Super-Hamiltonians for super-Macdonald polynomials
Explicit vertex-operator super-Hamiltonians are conjectured whose eigenfunctions are the super-Macdonald polynomials of earlier work.
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