A Family of Right Coideal Subalgebras of U_q(sl_(n+1))

The presented thesis describes a new family of spherical right coideal subalgebras of quantum universal enveloping algebras of type A_n. The description of the spherical right coideal subalgebras is given in terms of PBW-type elements. The representation theory is derived from quantum universal enveloping algebras of type A_n. The resulting quantum homogeneous space is compared with an already known one