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ON SEPARATION OF VARIABLES AND COMPLETENESS OF THE BETHE ANSATZ FOR QUANTUM N GAUDIN MODEL

Published online by Cambridge University Press:  01 February 2009

E. MUKHIN ,
V. TARASOV  and
A. VARCHENKO
E. MUKHIN
Affiliation:
Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis402 North Blackford St, Indianapolis, IN 46202-3216, USA e-mail: [email protected]
V. TARASOV
Affiliation:
St. Petersburg Branch of Steklov Mathematical InstituteFontanka 27, St. Petersburg, 191023, Russia e-mail: [email protected]
A. VARCHENKO
Affiliation:
Department of Mathematics, University of North Carolina at Chapel HillChapel Hill, NC 27599-3250, USA e-mail: [email protected]
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Abstract

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In this paper, we discuss implications of the results obtained in [5]. It was shown there that eigenvectors of the Bethe algebra of the quantum N Gaudin model are in a one-to-one correspondence with Fuchsian differential operators with polynomial kernel. Here, we interpret this fact as a separation of variables in the N Gaudin model. Having a Fuchsian differential operator with polynomial kernel, we construct the corresponding eigenvector of the Bethe algebra. It was shown in [5] that the Bethe algebra has simple spectrum if the evaluation parameters of the Gaudin model are generic. In that case, our Bethe ansatz construction produces an eigenbasis of the Bethe algebra.

Keywords

81R10 (17B10 81R12 34M35)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue A , February 2009 , pp. 137 - 145
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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