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Algebra i Analiz, 2010, Volume 22, Issue 3, Pages 177–190 (Mi aa1191)  
This article is cited in 24 scientific papers (total in 24 papers)

Research Papers

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

E. Mukhina, V. Tarasovba, A. Varchenkoc

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
Full-text PDF (618 kB) Citations (24)
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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
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 3, Pages 463–472
DOI: https://doi.org/10.1090/S1061-0022-2011-01152-5
Bibliographic databases:
Document Type: Article
Language: English
Citation: E. Mukhin, V. Tarasov, A. Varchenko, “Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\frak{gl}_N$”, Algebra i Analiz, 22:3 (2010), 177–190; St. Petersburg Math. J., 22:3 (2011), 463–472
Citation in format AMSBIB
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    • This publication is cited in the following 24 articles:
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