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

Abstract

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.

24 pages

Cited by in corpus (2)

• On quantum cluster algebras of finite type
• Examples of quantum cluster algebras associated to partial flag varieties