On the Wave Functions of Ruijsenaars Model Related to q-Analogue of Symmetric Space GL(n)/SO(n)
نویسنده
چکیده
In [1], the wave functions of quantum trigonometric n-particle Ruijsenaars model are defined as matrix elements of operators of representations of Cartan subalgebra between vectors invariant with respect to q-deformation U ′ q(son) of Lie algebra so(n). It was shown there, that the wave functions defined in such a way are simultaneous eigenfunctions of commuting set of Macdonald–Ruijsenaars difference operators. Using this information, the expressions for wave functions in terms of Macdonald polynomials were found. In this contribution, these expressions are obtained in a direct manner by using explicit expressions for invariant vectors in representation spaces in terms of Gel’fand–Tsetlin basis.
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