Drinfeld–Sokolov reduction in quantum algebras: canonical form of generating matrices

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Abstract

We define the second canonical forms for the generating matrices of the Reflection Equation algebras and the braided Yangians, associated with all even skew-invertible involutive and Hecke symmetries. By using the Cayley–Hamilton identities for these matrices, we show that they are similar to their canonical forms in the sense of Chervov and Talalaev (J Math Sci (NY) 158:904–911, 2008).

Keywords

Reflection Equation algebra Braided Yangian Second canonical form Quantum elementary symmetric functions Quantum power sums Cayley–Hamilton identity 

Mathematics Subject Classification

81R50 
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Notes

Acknowledgements

The work of D.T. was partially supported by the grant of the Simons foundation and the RFBR Grant 17-01-00366 A. The work of P.S. has been funded by the Russian Academic Excellence Project ’5-100’ and was also partially supported by the RFBR Grant 16-01-00562.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université de Valenciennes, EA 4015-LAMAVValenciennesFrance
  2. 2.Interdisciplinary Scientific Center Poncelet (ISCP, UMI 2615 du CNRS)MoscowRussian Federation
  3. 3.National Research University Higher School of EconomicsMoscowRussian Federation
  4. 4.Institute for High Energy PhysicsNRC “Kurchatov Institute”ProtvinoRussian Federation
  5. 5.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussian Federation

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