%0 Journal Article
%T Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases
%A Jan E. Grabowski
%A St¨¦phane Launois
%J Mathematics
%D 2009
%I arXiv
%R 10.1093/imrn/rnq153
%X We exhibit quantum cluster algebra structures on quantum Grassmannians $K_q[Gr(2,n)]$ and their quantum Schubert cells, as well as on $K_q[Gr(3,6)]$, $K_q[Gr(3,7)]$ and $K_q[Gr(3,8)]$. These cases are precisely those where the quantum cluster algebra is of finite type and the structures we describe quantize those found by Scott for the classical situation.
%U http://arxiv.org/abs/0912.4397v1