A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras

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dc.contributor.authorGillespie, Jason Michaelen
dc.contributor.committeechairShimozono, Mark M.en
dc.contributor.committeememberGreen, Edward L.en
dc.contributor.committeememberParry, Charles J.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.committeememberHaskell, Peter E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2011-08-22T18:51:44Zen
dc.date.adate2003-12-09en
dc.date.available2011-08-22T18:51:44Zen
dc.date.issued2003-12-02en
dc.date.rdate2003-12-09en
dc.date.sdate2003-12-04en
dc.description.abstractWe prove the positivity of Lusztig's q-analogue of weight multiplicity in a purely combinatorial way for rank 2 Lie algebras. Each summand in the polynomial can be interpreted as a linear combination of positive roots. We prove that all negative coefficients are cancelled in the polynomial. Further, the analysis of the root systems allows us to state formulae for every coefficient in Lusztig's q-analogue for rank 2 Lie algebras.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.otheretd-12042003-173047en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12042003-173047en
dc.identifier.urihttp://hdl.handle.net/10919/11071en
dc.publisherVirginia Techen
dc.relation.haspartKostkarevised.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectLusztig q-analogueen
dc.subjectCombinatoricsen
dc.subjectLie Algebrasen
dc.subjectRoot Systemsen
dc.titleA Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebrasen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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