The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group
The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group
We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum groups \mathcal O_q(\mathit{GL}_t(K)) and \mathcal O_q(\mathit{SL}_t(K)) on the quantized algebra \mathcal O_q(M_{m,t}(K)) \otimes \mathcal O_q(M_{t, n}(K)) . (Here K is an arbitrary field and q an arbitrary nonzero scalar.) In both cases, the set of …