Drinfeld–Sokolov reduction in quantum algebras: canonical form of generating matrices
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).
KeywordsReflection Equation algebra Braided Yangian Second canonical form Quantum elementary symmetric functions Quantum power sums Cayley–Hamilton identity
Mathematics Subject Classification81R50
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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