Ring theoretic properties of quantum grassmannians

The m × n quantum grassmannian, G q (m, n), with m ≤ n, is the subalgebra of the algebra O q (M mn) of quantum m × n matrices that is generated by the maximal m×m quantum minors. Several properties of G q (m, n) are established. In particular, a k-basis of G q (m, n) is obtained, and it is shown that G q (m, n) is a noetherian domain of Gelfand-Kirillov dimension m(n − m) + 1. The algebra G q (m, n) is identified as the subalgebra of coinvariants of a natural left coaction of O q (SL m) on O q (M mn) and it is shown that G q (m, n) is a maximal order.