Abstract

Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases

International Mathematics Research Notices, 10 (2011), 2230-2262, arXiv:0912.4397

We exhibit quantum cluster algebra structures on quantum Grassmannians Kq[Gr(2,n)] and their quantum Schubert cells, as well as on Kq[Gr(3,6)], Kq[Gr(3,7)] and Kq[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.