Quantum Deformation of the Grassmannian Manifold

Quantum deformation of the flag variety

“…We will construct the quantum flag ring as a subalgebra of k q [SL n (k)], the quantum SL n (k) and we then will exhibit it in terms of generators and relations in the case in which k q is replaced by a suitable local ring in k(q). These results are a generalization of those obtained for the quantum grassmannian in [4]. …”

“…j s ) (see remark (3.2)). The argument that we used in [4] for the quantum grassmannian, here will not work here as it is. Theorem (3.8).…”

“…Theorem 3.8 gives the commutation relations for two quantum determinants in the general case. The proof of the corresponding theorem in [4] cannot be adapted in our present case where the determinant have different ranks.…”

“…This paper comes as a generalization of [4] where we give a deformation of the grassmannian manifold.…”

“…In section 4 we derive the Plücker and incidence relations with a method which is different from the one used in [4]. This allows us to get more explicit formulas.…”