We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum groups Oq(GLt(K)) and Oq(SLt(K)) on the quantized algebra Oq(Mm,t(K)) ⊗ Oq(Mt, n(K)). (Here K is an arbitrary field and q an arbitrary nonzero scalar.) In both cases, the set of co-invariants is a subalgebra of Oq(Mm,t(K)) ⊗ Oq(Mt, n(K)), which we identify.
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Thomas H. Lenagan, Kenneth R. Goodearl, Laurent Rigal, The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group. Publ. Res. Inst. Math. Sci. 36 (2000), no. 2, pp. 269–296DOI 10.2977/PRIMS/1195143104