Title page for ETD etd-12042003-173047


Type of Document Dissertation
Author Gillespie, Jason Michael
URN etd-12042003-173047
Title A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Shimozono, Mark M. Committee Chair
Brown, Ezra A. Committee Member
Green, Edward L. Committee Member
Haskell, Peter E. Committee Member
Parry, Charles J. Committee Member
Keywords
  • Lusztig q-analogue
  • Combinatorics
  • Lie Algebras
  • Root Systems
Date of Defense 2003-12-02
Availability unrestricted
Abstract
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.

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