Please use this identifier to cite or link to this item: http://hdl.handle.net/2381/44126
Title: On Generalized Minors and Quiver Representations
Authors: Rupel, Dylan
Stella, Salvatore
Williams, Harold
First Published: 12-Apr-2018
Publisher: Oxford University Press (OUP)
Citation: International Mathematics Research Notices, 2018, rny053
Abstract: The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, defining a Coxeter element and thereby a double Bruhat cell. We use this realization to connect representations of the quiver with those of the group. We show that cluster variables of preprojective (resp. postinjective) quiver representations are realized by generalized minors of highest-weight (resp. lowest-weight) group representations, generalizing results of Yang-Zelevinsky in finite type. In type $A_n^{\!(1)}$ and finitely many other affine types, we show that cluster variables of regular quiver representations are realized by generalized minors of group representations that are neither highest- nor lowest-weight; we conjecture this holds more generally.
DOI Link: 10.1093/imrn/rny053
eISSN: 1687-0247
Links: https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rny053/4969402
http://hdl.handle.net/2381/44126
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2018, Oxford University Press (OUP). Deposited with reference to the publisher’s open access archiving policy. (http://www.rioxx.net/licenses/all-rights-reserved)
Appears in Collections:Published Articles, Dept. of Mathematics

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