2023/12/28 by Liana Heuberger, Heuberger, Liana, Elana Kalashnikov +1
Computer Science · Mathematics · #13A50 #14L24 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2312.17224
openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new combinatorial structure of linked tableaux, which generalize the semi-standard tableaux that index a SAGBI basis of the Plücker coordinate ring of a flag variety. We show that linked tableaux index Domokos-Zubkov semi-invariants, which span the semi-invariant ring of a quiver. The semi-invariant ring of a quiver coincides in many cases with the Cox ring of an associated quiver moduli space. We show that these semi-invariants satisfy straightening laws. In the case of the generalized Kronecker quiver, we prove that the semi-invariants associated to semi-standard linked tableaux are a (possibly infinite) SAGBI basis. For the generalized Kronecker quiver with dimension vector (2,2), we show that the SAGBI basis is finite and describe it explicitly.