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

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

2009-12-22

arxiv.org/abs/0912.4397v1

International Mathematics Research Notices, no. 10 (2011): 2230-2262

Mathematics

Quantum Algebra

24 pages

Scientific paper

10.1093/imrn/rnq153

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.

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