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dc.contributor.authorLenart, Cristian
dc.contributor.authorNaito, Satoshi
dc.contributor.authorSagaki, Daisuke
dc.contributor.authorSchilling, Anne
dc.contributor.authorShimozono, Mark
dc.date.accessioned2012-12-22T12:00:00Z
dc.date.accessioned2016-10-05T14:13:52Z
dc.date.available2012-12-22T12:00:00Z
dc.date.available2016-10-05T14:13:52Z
dc.date.issued2012
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1050
dc.descriptionResearch in Pairs 2012en_US
dc.description.abstractWe consider two lifts of the parabolic quantum Bruhat graph, one into the Bruhat order in the affine Weyl group and the other into a level-zero weight poset first considered by Littelmann. The lift into the affine Weyl group gives rise to Diamond Lemmas for the parabolic quantum Bruhat graph. Littlemann's poset is defined on Lakshmibai-Seshadri paths for arbitrary (not necessarily dominant) weights. Here we consider this poset for level-zero weights and determine its local structure (such as cover relations) in terms of the parabolic quantum Bruhat graph. Littelmann had not determined the local structure of this poset. In addition, we show a generalization of results by Deodhar, coined the tilted-Bruhat theorem, which involves the compatibility of the quantum Bruhat graph with the cosets for every parabolic subgroup of the Weyl group. We will use the results in this paper in a second paper to establish the equality between the Macdonald polynomials $P_\lambda (q,t)$ specialized at $t = 0$ and $X_\lambda (q)$ which is the graded character of a simple Lie algebra coming from tensor products of Kirillov-Reshetikhin (KR) modules.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2012,18
dc.subjectParabolic quantumen_US
dc.subjectBruhat graphen_US
dc.subjectLakshmibai-Seshadri pathsen_US
dc.subjectLittelmann path modelen_US
dc.subjectCrystal basesen_US
dc.subjectDeodhar's liften_US
dc.titleA Uniform Model for Kirillov-Reshetikhin Crystals I: Lifting the Parabolic Quantum Bruhat Graphen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2012-18
local.scientificprogramResearch in Pairs 2012
local.series.idOWP-2012-18
local.subject.msc05
local.subject.msc33
local.subject.msc20
dc.identifier.urnurn:nbn:de:101:1-2013020112017
dc.identifier.ppn1652029230


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