Twisted Yangians, Twisted Quantum Loop Algebras and Affine Hecke Algebras of Type Bc
نویسنده
چکیده
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.
منابع مشابه
From quantum loop algebras to Yangians
The main purpose of this note is to give a proof of a statement of V. Drinfeld in [Dr1] regarding Yangians and quantum loop algebras, namely how the former can be constructed as limit forms of the latter. We also apply the same ideas to twisted quantum loop algebras to recover the (non-twisted) Yangians.
متن کاملFrom twisted quantum loop algebras to twisted Yangians
We prove how the Yangian of glN in its RTT presentation and Olshanski’s twisted Yangians for the orthogonal and symplectic Lie algebras can be obtained by a degeneration process from the corresponding quantum loop algebra and some of its twisted analogues.
متن کاملSe p 20 09 Representations of twisted q - Yangians by Lucy Gow and
The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with glN . We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the symplectic Lie algebras sp2n. The representations are parameterized by their highest weights or by their Drinfeld polynomials. In the simplest case of sp2 we give an e...
متن کاملRepresentations of twisted q - Yangians by Lucy Gow and
The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with glN . We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the symplectic Lie algebras sp2n. The representations are parameterized by their highest weights or by their Drinfeld polynomials. In the simplest case of sp2 we give an e...
متن کاملDrinfeld J Presentation of Twisted Yangians
We present a quantization of a Lie coideal structure for twisted half-loop algebras of finite-dimensional simple complex Lie algebras. We obtain algebra closure relations of twisted Yangians in Drinfeld J presentation for all symmetric pairs of simple Lie algebras and for simple twisted even half-loop Lie algebras. We provide the explicit form of the closure relations for twisted Yangians in Dr...
متن کامل