Realizations of quantum hom-spaces, invariant theory, and quantum determinantal ideals (Q1604376)

The standard definition of the quantum matrix bialgebra \(E_R\) associated to a Hecke operator \(R\) generalised is in this paper to define the function algebra \(M_{RS}\) on the quantum space of homomorphisms of two quantum spaces associated to two Hecke operators \(R\) and \(S\). Thus \(M_{RS}\) is a deformation of the function algebra of the variety of matrices of a certain degree. \(M_{RS}\) is defined both as a factor algebra and as a subalgebra of the tensor algebra. Various properties of \(M_{RS}\) are proved, and the versions of the fundamental theorems of invariant theory proved for quantum matrices [see e.g. \textit{K. R. Goodearl, T. H. Lenagan} and \textit{L. Rigal}, Publ. Res. Inst. Math. Sci. 36, 269--296 (2000; Zbl 0972.16022)] are extended to this more general setting.