E. Mukhin, V. Tarasov, A. Varchenko, “Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of <nobr>$\frak{gl}_N$</nobr>”, Algebra i Analiz, 2010, Volume 22, Issue 3,Pages <nobr>177

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Research Papers

Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\frak{gl}_N$

E. Mukhin^a, V. Tarasov^ba, A. Varchenko^c

^a Department of Mathematical Sciences, Indiana University — Purdue University Indianapolis, Indianapolis, IN, USA
^b St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
^c Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

Abstract: It is shown that the Gaudin Hamiltonians $H_1,\dots,H_n$ generate the Bethe algebra of the $n$-fold tensor power of the vector representation of $\frak{gl}_N$. Surprisingly, the formula for the generators of the Bethe algebra in terms of the Gaudin Hamiltonians does not depend on $N$. Moreover, this formula coincides with Wilson's formula for the stationary Baker–Akhiezer function on the adelic Grassmannian.

Keywords: Gaudin model, Bethe algebra, Calogero–Moser space.

Received: 15.11.2009

Language: English