Chapter

Algebra, Arithmetic, and Geometry

Volume 270 of the series Progress in Mathematics pp 383-398

Date:

A Generalization of the Capelli Identity

  • E. MukhinAffiliated withDepartment of Mathematical Sciences, Indiana University – Purdue University Indianapolis Email author 
  • , V. TarasovAffiliated withDepartment of Mathematical Sciences, Indiana University – Purdue University IndianapolisSt. Petersburg Branch of Steklov Mathematical Institute
  • , A. VarchenkoAffiliated withDepartment of Mathematics, University of North Carolina at Chapel Hill

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Summary

We prove a generalization of the Capelli identity. As an application we obtain an isomorphism of the Bethe subalgebras actions under the \(({g l}_{N},{g l}_{M})\) duality.

Key words

Capelli identity Gaudin model \(({g l}_{N} g {l}_{M})\) duality