Cluster algebras, invariant theory, and Kronecker coefficients II
We prove that the semi-invariant ring of the standard representation space of the l-flagged m-arrow Kronecker quiver is an upper cluster algebra for any l,m∈N. The quiver and cluster are explicitly given. We prove that the quiver with its rigid potential is a polyhedral cluster model. As a consequen...
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Published in | Advances in mathematics (New York. 1965) Vol. 341; pp. 536 - 582 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
07.01.2019
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Subjects | |
Online Access | Get full text |
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Summary: | We prove that the semi-invariant ring of the standard representation space of the l-flagged m-arrow Kronecker quiver is an upper cluster algebra for any l,m∈N. The quiver and cluster are explicitly given. We prove that the quiver with its rigid potential is a polyhedral cluster model. As a consequence, to compute each Kronecker coefficient gμ,νλ with λ at most m parts, we only need to count lattice points in at most m! fiber (rational) polytopes inside the g-vector cone, which is explicitly given. |
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ISSN: | 0001-8708 1090-2082 |
DOI: | 10.1016/j.aim.2018.10.042 |