Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\mathfrak {gl}_N$
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- by E. Mukhin, V. Tarasov and A. Varchenko
- St. Petersburg Math. J. 22 (2011), 463-472
- DOI: https://doi.org/10.1090/S1061-0022-2011-01152-5
- Published electronically: March 18, 2011
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Abstract:
It is shown that the Gaudin Hamiltonians $H_1$, …, $H_n$ generate the Bethe algebra of the $n$-fold tensor power of the vector representation of $\mathfrak {gl}_N$. 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.References
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Bibliographic Information
- E. Mukhin
- Affiliation: Department of Mathematical Sciences, Indiana University — Purdue University Indianapolis, 402 North Blackford St., Indianapolis, Indiana 46202-3216
- MR Author ID: 317134
- Email: mukhin@math.iupui.edu
- V. Tarasov
- Affiliation: Department of Mathematical Sciences, Indiana University — Purdue University Indianapolis, 402 North Blackford St., Indianapolis, Indiana 46202-3216
- Address at time of publication: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Email: vt@math.iupui.edu, vt@pdmi.ras.ru
- A. Varchenko
- Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-325
- MR Author ID: 190269
- Email: anv@email.unc.edu
- Received by editor(s): November 15, 2009
- Published electronically: March 18, 2011
- Additional Notes: E. Mukhin was supported in part by NSF grant DMS-0900984
V. Tarasov was supported by NSF grant DMS-0901616
A. Varchenko was supported by NSF grant DMS-0555327 - © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 463-472
- MSC (2010): Primary 82C23, 81Q12
- DOI: https://doi.org/10.1090/S1061-0022-2011-01152-5
- MathSciNet review: 2729945
Dedicated: To Ludwig Dmitrievich Faddeev on his 75th birthday