Twisted Yangians, twisted quantum loop algebras and affine Hecke algebras of type $BC$

Abstract

We study twisted Yangians of type AIII which have appeared in the literature under the name of reflection algebras. They admit q-versions which are new twisted quantum loop algebras. We explain how these can be defined equivalently either via the reflection equation or as coideal subalgebras of Yangians of gln (resp. of quantum loop algebras of gln). The connection with affine Hecke algebras of type BC comes from a functor of Schur-Weyl type between their module categories.