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

Dimitri Gurevich (1) , Pavel Saponov , Dmitry Talalaev

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

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).

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

Domaines: Mathématiques [math]

Dimitri Gurevich, Pavel Saponov, Dmitry Talalaev. Drinfeld–Sokolov reduction in quantum algebras: canonical form of generating matrices. Letters in Mathematical Physics, 2018, 108 (10), p. 2303-2314. ⟨10.1007/s11005-018-1084-x⟩. ⟨hal-03165329⟩