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arXiv · 0912.4397

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

Jan E. Grabowski·Stéphane Launois
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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.

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Jan E. Grabowski, Stéphane Launois. 2009-12-22. Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases. https://doi.org/10.1093/imrn%2Frnq153

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