The automorphism group of the quantum grassmannian

Abstract

AbstractThe automorphism group of a quantised coordinate algebra is usually much smaller than that of its classical counterpart. Nevertheless, these automorphism groups are often very difficult to calculate. In this paper, we calculate the automorphism group of the quantum grassmannian in the case that the deformation parameter is not a root of unity. The main tool employed is the dehomogenisation equality which shows that a localisation of the quantum grassmannian is equal to a skew Laurent extension of quantum matrices. This equality is used to connect the automorphism group of the quantum grassmannian with that of quantum matrices, where the automorphism group is known.