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

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

We 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. Fu...

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Bibliographic Details
Main Author: Gillespie, Jason Michael
Other Authors: Mathematics
Format: Others
Published: Virginia Tech 2011
Subjects:
Lusztig q-analogue
Combinatorics
Lie Algebras
Root Systems
Online Access:http://hdl.handle.net/10919/11071
http://scholar.lib.vt.edu/theses/available/etd-12042003-173047
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spelling ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-110712020-09-29T05:32:16Z A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras Gillespie, Jason Michael Mathematics Shimozono, Mark M. Green, Edward L. Parry, Charles J. Brown, Ezra A. Haskell, Peter E. Lusztig q-analogue Combinatorics Lie Algebras Root Systems We 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. Ph. D. 2011-08-22T18:51:44Z 2011-08-22T18:51:44Z 2003-12-02 2003-12-04 2003-12-09 2003-12-09 Dissertation etd-12042003-173047 http://hdl.handle.net/10919/11071 http://scholar.lib.vt.edu/theses/available/etd-12042003-173047 Kostkarevised.pdf In Copyright http://rightsstatements.org/vocab/InC/1.0/ ETD application/pdf Virginia Tech
collection NDLTD
format Others
sources NDLTD
topic Lusztig q-analogue
Combinatorics
Lie Algebras
Root Systems
spellingShingle Lusztig q-analogue
Combinatorics
Lie Algebras
Root Systems
Gillespie, Jason Michael
A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
description We 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. === Ph. D.
author2 Mathematics
author_facet Mathematics
Gillespie, Jason Michael
author Gillespie, Jason Michael
author_sort Gillespie, Jason Michael
title A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
title_short A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
title_full A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
title_fullStr A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
title_full_unstemmed A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
title_sort combinatorial proof of the positivity of the lusztig q-analogue of weight multiplicity for rank 2 lie algebras
publisher Virginia Tech
publishDate 2011
url http://hdl.handle.net/10919/11071
http://scholar.lib.vt.edu/theses/available/etd-12042003-173047
work_keys_str_mv AT gillespiejasonmichael acombinatorialproofofthepositivityofthelusztigqanalogueofweightmultiplicityforrank2liealgebras
AT gillespiejasonmichael combinatorialproofofthepositivityofthelusztigqanalogueofweightmultiplicityforrank2liealgebras
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