The invariant prime ideals of \(O_q({\mathcal M}_{m,p}(\mathbb{C}))\). (Q1425094)

Let \({\mathcal O}_q({\mathcal M}_{m,p}(\mathbb{C}))\) be the complex algebra of functions on quantum \((m\times n)\)-matrices with canonical generators \(Y_{i,j}\) where \( 1\leqslant i\leqslant m\), \(1\leqslant j\leqslant n\). It is assumed that \(q\) is transcendental over the field of rational numbers. Denote by \(H\) the group of all automorphisms of the form \(Y_{ij}\mapsto a_ib_jY_{ij}\), where \(a_1,\dots,a_m,b_1,\dots,b_n\in\mathbb{C}^*\). The main result of the paper shows that each \(H\)-invariant prime ideal of \({\mathcal O}_q({\mathcal M}_{m,p}(\mathbb{C}))\) is generated as a right or a left ideal by quantum minors constructed on the canonical generators \(Y_{i,j}\).