Quantizing Grassmannians, Schubert cells and cluster algebras
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Thu, 21/01/2010 14:30 |
Jan Grabowski (Oxford) |
Representation Theory Seminar  |
L3 |
| The quantum Grassmannians and their quantum Schubert cells are well-known and important examples in the study of quantum groups and quantum geometry. It has been known for some time that their classical counterparts admit cluster algebra structures, which are closely related to positivity properties. Recently we have shown that in the finite-type cases quantum Grassmannians admit quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky. We will describe these structures explicitly and also show that they naturally induce quantum cluster algebra structures on the quantum Schubert cells. This is joint work with S. Launois. | |||