Abstract
Multiparametric quantum semigroups Mqˆ,pˆ(n) are generalization of the one-parameter general linear semigroups Mq(n), where qˆ=(qij) and pˆ=(pij) are 2n2 parameters satisfying certain conditions. In this paper, we study the algebra of multiparametric Manin matrices using the R-matrix method. The systematic approach enables us to obtain several classical identities such as Muir's identities, Newton's identities, Capelli-type identities, Cauchy-Binet's identity both for determinant and permanent as well as a rigorous proof of the MacMahon master equation for the quantum algebra of multiparametric Manin matrices. Some of the generalized identities are also lifted to multiparameter q-Yangians.
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