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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 10/1997

E.K.Sklyanin
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GENERATING FUNCTION OF CORRELATORS
IN THE $sl_2$ GAUDIN MODEL

This preprint was accepted June, 1997.

Contact: ` E.K.Sklyanin `

ABSTRACT:
For the $sl_2$ Gaudin model (degenerated quantum integrable XXX spin chain)
an exponential generating function of correlators is calculated explicitely.
The calculation relies on the Gauss decomposition for the $SL_2$ loop group.
From the generating function a new explicit expression for the correlators
is derived from which the determinant formulas for the norms of Bethe
eigenfunctions due to Richardson and Gaudin are obtained.

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