Inverse problem for sl(2) lattices

We consider the inverse problem for periodic sl(2) lattices as a canonical transformation from the separation to local variables. A new concept of a factorized separation chain is introduced allowing to solve the inverse problem explicitly. The method is applied to an arbitrary representation of the corresponding Sklyanin algebra.Comment: 16 pages, LaTeX, talk at SPT 2002, 19-26/5, Cala Gonone, Sardinia; corrected voffset-optio

Brushless asynchronous induction machines with leading VAR capability

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Factorisation of Macdonald polynomials

We discuss the problem of factorisation of the symmetric Macdonald polynomials and present the obtained results for the cases of 2 and 3 variables.Comment: 13 pages, LaTex, no figure

Gauss hypergeometric function and quadratic RR-matrix algebras

We consider representations of quadratic $R$-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with W. Miller's treatment of Lie algebras of first order differential operators will be discussed.Comment: 26 page