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. 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2003

Author dc:creator

• Gillespie, Jason Michael

Chair dc:contributor.committeechair

• Shimozono, Mark M.

Committee members dc:contributor.committeemember

• Green, Edward L.
• Parry, Charles J.
• Brown, Ezra A.
• Haskell, Peter E.

• Lusztig q-analogue
• Combinatorics
• Lie Algebras
• Root Systems

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-12042003-173047

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/11071