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Regular version of the site

Article

Bethe subalgebras in Braided Yangians and Gaudin-type models

Communications in Mathematical Physics. 2020. Vol. 374. No. 2. P. 689-704.
Saponov P. A., Slinkin A., Gurevich D.

In Gurevich and Saponov (J Geom Phys 138:124–143, 2019) the notion of braided Yangians of Reflection Equation type was introduced. Each of these algebras is associated with an involutive or Hecke symmetry R. In these algebras quantum analogs of certain symmetric polynomials (elementary symmetric ones, power sums) were defined. In the present paper we show that these quantum symmetric polynomials commute with each other and consequently generate a commutative Bethe subalgebra. As an application, we get some Gaudin-type models.