Capelli identity on multiparameter quantum linear groups

Abstract

Abstract. A quantum Capelli identity is given on the multiparameter quantum general linear group based on the (pij, u)-condition. The multiparameter quantum Pfaffian of the (pij, u)-quantum group is also introduced and the transformation under the congruent action is given. Generalization to the multiparameter hyper-Pfaffian and relationship with the quantum minors are also investigated.