Computing of the number of right coideal subalgebras of Uq(so2n+1)

In this paper we complete the classification of right coideal subalgebras containing all grouplike elements for the multiparameter version of the quantum group Uq(so2n+1), qt≠1. It is known that every such subalgebra has a triangular decomposition U=U−HU+, where U− and U+ are right coideal subalgebras of negative and positive quantum Borel subalgebras. We found a necessary and sufficient condition for the above triangular composition to be a right coideal subalgebra of Uq(so2n+1) in terms of the PBW-generators of the components. Furthermore, an algorithm is given that allows one to find an explicit form of the generators. Using a computer realization of that algorithm, we determined the number rn of different right coideal subalgebras that contain all grouplike elements for n⩽7. If q has a finite multiplicative order t>4, the classification remains valid for homogeneous right coideal subalgebras of the multiparameter version of the Lusztig quantum group uq(so2n+1) (the Frobenius–Lusztig kernel of type Bn) in which case the total number of homogeneous right coideal subalgebras and the particular generators are the same.