Block-Toeplitz determinants, chess tableaux, and the type $\hat{A_1}$ Geiss-Leclerc-Schroer $ϕ$-map

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dc.creatorScott, Jeanne
dc.date2007-07-20
dc.date.accessioned2026-07-07T08:19:23Z
dc.date.available2026-07-07T08:19:23Z
dc.descriptionWe evaluate the Geiss-Leclerc-Schroer $ϕ$-map for shape modules over the preprojective algebra $Λ$ of type $\hat{A_1}$ in terms of matrix minors arising from the block-Toeplitz representation of the loop group $\SL_2(\mathcal{L})$. Conjecturally these minors are among the cluster variables for coordinate rings of unipotent cells within $\SL_2(\mathcal{L})$. In so doing we compute the Euler characteristic of any generalized flag variety attached to a shape module by counting standard tableaux of requisite shape and parity; alternatively by counting chess tableaux of requisite shape and content.
dc.identifierhttps://arxiv.org/abs/0707.3046
dc.identifierhttp://arxiv.org/abs/0707.3046
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134746
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject22E67; 05E10; 15A57; 16G20; 14L40; 05E05
dc.titleBlock-Toeplitz determinants, chess tableaux, and the type $\hat{A_1}$ Geiss-Leclerc-Schroer $ϕ$-map
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