Canonical bases of a coideal subalgebra in $U_q(\mathfrak{sl}_2)$

摘要: We consider tensor products of finite-dimensional representations a coideal subalgebra in $U_{q}(\mathfrak{sl}_2)$. present an explicit expression for the dual canonical bases through diagrammatic presentation. show that decomposition and action have integral positive properties. As application, we eigensystem generator on bases. provide all eigenvalues obtain eigenfunction largest eigenvalue. The sum components this is conjectured to be equal total number arrangements bishops with certain symmetry.