- Reflection equation algebras, coideal subalgebras, and their centres
- Selecta Mathematica-New Series
- Volume | Issue number
- 15 | 4
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
Reflection equation algebras and related U-q(g)-comodule algebras appear in various constructions of quantum homogeneous spaces and can be obtained via transmutation or equivalently via twisting by a cocycle. In this paper we investigate algebraic and representation theoretic properties of such so called 'covariantized' algebras, in particular concerning their centres, invariants, and characters. The locally finite part F-l(U-q(g)) of U-q(g) with respect to the left adjoint action is a special example of a covariantized algebra. Generalising Noumi's construction of quantum symmetric pairs we define a coideal subalgebra B-f of U-q(g) for each character f of a covariantized algebra. We show that for any character f of F-l(U-q(g)) the centre Z(B-f) canonically contains the representation ring Rep(g) of the semisimple Lie algebra g. We show moreover that for g = sl(n)(C) such characters can be constructed from any invertible solution of the reflection equation and hence we obtain many new explicit realisations of Rep(sl(n)(C)) inside U-q(sl(n)(C)). As an example we discuss the solutions of the reflection equation corresponding to the Grassmannian manifold Gr(m, 2m) of m-dimensional subspaces in C-2m.
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