From the 1 of 6 linked papers with an AI index.
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Cluster Algebras for Bosonic Plethysm
Yelin Fan, Jiarui Fei
Let be an algebraically closed field of characteristic zero, let and , and set \[ \mathcal R_{\ell,m}=\operatorname{Sym}(\operatorname{Sym}^2V\oti…
A Polyhedral Formula for Kronecker Coefficients via Cluster Algebras
Jiarui Fei, Chenxin Xue
Let \[ \Bbbk[\Bbbk^3\otimes\Bbbk^2\otimes\Bbbk^2]^{U_3\times U_2\times U_2}. \] We construct an ordinary cluster family with Markov principal part. At , the intersection of i…
Crystal Structure of Upper Cluster Algebras
Jiarui Fei
We describe the upper seminormal crystal structure for the -supported -vectors for any quiver with potential with reachable frozen vertices, or equivalently for the tropica…
On the Orthogonal Projections
Jiarui Fei
For any rigid presentation , we construct an orthogonal projection functor to left adjoint to the natural embedding. We establish a bijection between presen…
On the General Ranks of QP Representations
Jiarui Fei
We propose a mutation formula for the general rank from a principal component of representations to another one for a quiver with potential. We give s…