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Cluster algebras are closely related to totally positivity in algebraic groups and canonical bases in quantum groups. Is there some relation between cluster algebras and crystal graphs? Can the cryst …

Let $H$ be a hereditary algebra of Dynkin type. There is a cluster category $\mathcal{C}_H$ defined by Aslak Bakke Buan, Robert Marsh, Markus Reineke, Idun Reiten, and Gordana Todorov in Tilting theor …

Super Grassmannians are introduced by Manin, see for example. We have Plucker relation for Grassmannian. Are there some references about super Plucker relations for super Grassmannian? Thank you ver …

Let $X$ be a Poisson variety. There is a concept "cluster algebra structure compatible with Poisson structure" introduced in the paper. Suppose that we construct a maximal independent set of functio …

Are there some references about tropical cluster algebras and tropical Laurent phenomenon? I searched on Google but only found one paper: Tropical Plucker functions and their bases . Thank you very …

Geometric realizations of cluster categories of simply-laced types are studied in the following papers. Philippe Caldero, Frédéric Chapoton, and Ralf. Schiffler, Quivers with relations arising from …

I am trying to understand the proof of Laurent phenomenon of cluster algebras in the book (Sergey Fomin, Lauren Williams, Andrei Zelevinsky, Introduction to Cluster Algebras. Chapters 1-3, arXiv:1608. …

In the paper, (5.28) on page 35 is a formula which translate cluster A-coordinates to cluster X-coordinates: \begin{align} x_i = \prod_{i \to j} a_j. \end{align} Is there a formula which translate …

In the paper, the orthosymplectic supergroup $OSP(2p|n)$ is defined as follows. Let $A = A_0 \oplus A_1$ be a supercommutative superalgebra, where elements in $A_0$ are even and elements in $A_1$ are …

In the paper The Amplituhedron , Nima Arkani-Hamed and Jaroslav Trnka introduced the geometric object amplituhedron. It is defined as follows (see also the lecture notes). Let $Z$ be a $(k+m)\times …

I am reading the lecture notes and would like to know more about canonical basis. What are the relations among canonical basis, dual canonical basis, Semicanonical Basis, dual semicanonical bases? …

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 …

In Cluster algebra III by Berenstein-Fomin-Zelevinsky, Theorem 2.10, for any pair of reduced words $(u,v)$, they constructed an initial seed for the cluster algebra $\mathbb{C}[B^{u,v}]$, where $B^{u, …

Let $Mat_3$ be the set of all 3 by 3 matrices. I have some questions on the cluster algebra structure on the coordinate ring of $Mat_3$. We use $\Delta_{j_1\ldots j_n}^{i_1\ldots i_n}$ to denote the …

In the webpage, there is a result: Theorem 1. Coefficient free cluster algebras without frozen variables are in bijection with Dynkin diagrams of type $A_n$, $B_n$, $C_n$, $D_n$, $E_6, E_7, E_8$, $F_ …