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Tagged with cluster-algebras grassmannians
4 questions
2
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257
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Grassmannian $\mathrm{Gr}(k, \pm \infty)$ in infinite dimension
$\DeclareMathOperator\Gr{Gr}$The Grassmnnian variety $\Gr(k,n)$ is the set of $k$-dimensional subspaces of $\mathbb{C}^n$. The coordinate ring $\mathbb{C}[\Gr(k,n)]$ is generated by Plucker ...
- 6,211
8
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1
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Grassmannian cluster algebra of infinite type has no trees in its mutation class
The question is why the statement in the title is true (is it?).
To elaborate, recall that Grassmannian cluster algebra, according to Scott`s paper Grassmannians and Cluster Algebras, is the cluster ...
- 3,186
2
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Multiplication formula in Grassmannian cluster categories
Grassmannian cluster categories are studied in A categorification of Grassmannian cluster algebras and Cluster categories from Grassmannians and root combinatorics. The category $CM(B_{k,n})$ of Cohen-...
- 6,211
19
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Is it possible that the GHKK canonical basis for cluster algebras is the Lusztig/Kashiwara dual canonical basis?
Gross-Hacking-Keel-Kontsevich (https://arxiv.org/abs/1411.1394) constructed a canonical basis (the so-called “theta basis”) for a cluster algebra, at least assuming it satisfies a certain ...
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