Marti L. McClard, "Picturing Representations of Simple Lie Algebras of Rank Two," defended April 2000.
L. Wyatt Alverson II, "Distributive Lattices and Representations of the Rank Two Simple Lie Algebras," defended July 2003.
Matthew Ross Gilliland, "Distributive Lattices and Weyl Characters of Exotic Type F4," defended April 2008.

[0]  "Solitary bases for irreducible representations of semisimple Lie algebras"
        Refereed extended abstract for a talk given at the Formal Power Series and Algebraic Combinatorics
        Conference held at the Fields Institute and the Univ. of Toronto, 1998.   PDF, 12 pp.

[1]  "Symplectic analogs of the distributive lattices L(m,n)"
        Journal of Combinatorial Theory Series A  88 (1999), 217-234.

[2]  "Explicit constructions of the fundamental representations of the symplectic Lie algebras"
        Journal of Algebra  233 (2000), 37-64.

[3]  "Extremal properties of bases for representations of semisimple Lie algebras"
        Journal of Algebraic Combinatorics  17 (2003), 255-282.

[4]  "Constructions of representations of o(2n+1,C) that imply Molev and Reiner-Stanton lattices are strongly Sperner"
        With S. J. Lewis and R. Pervine.
        Discrete Mathematics  263 (2003), 61-79.

[5]  "Solitary and edge-minimal bases for representations of the simple Lie algebra G2"
        With S. J. Lewis and R. Pervine.
        Discrete Mathematics  306 (2006), 1285-1300.

[6]  "Extremal bases for the adjoint representations of the simple Lie algebras"
        Communications in Algebra  34 (2006), 3705-3742.

[7]  "Constructions of representations of rank two semisimple Lie algebras with distributive lattices"
        With L. W. Alverson II, S. J. Lewis, and R. Pervine.
        Electronic Journal of Combinatorics  13 (2006), #R109.   PDF, 44 pp.

[8]  "Eriksson's numbers game and finite Coxeter groups"
        European Journal of Combinatorics  29 (2008), 1764-1781.
        Available online November 2007, doi:10.1016/j.ejc.2007.06.029
        Also available on the arXiv as 0710.0173, 18 pp.

[8.5]  "Eriksson's numbers game on certain edge-weighted three-node cyclic graphs"
          PDF Preprint, 5 pp.   Also available on the arXiv as 0708.0880, 5 pp.
          This manuscript provides some supporting details for [8].

[9]  "Distributive lattices defined for representations of rank two semisimple Lie algebras"
        With L. W. Alverson II, S. J. Lewis, M. McClard, R. Pervine, R. A. Proctor, and N. J. Wildberger.
        SIAM Journal on Discrete Mathematics  23 (2009), 527-559.
        PDF Preprint, 33 pp.   Also available on the arXiv as 0707.2421, 33 pp.

[10]  "Root systems for asymmetric geometric representations of Coxeter groups"
          Accepted and to appear in Communications in Algebra.
          PDF Preprint, 15 pp.   Also available on the arXiv as 0707.3310, 15 pp.

[11]  "The numbers game and Dynkin diagram classification results"
          With Kimmo Eriksson.   PDF Preprint, 20 pp.   Also available on the arXiv as 0810.5371, 20 pp.

[11.5]  "Convergent and divergent numbers games for certain collections of edge-weighted graphs"
            PDF Preprint, 24 pp.   Also available on the arXiv as 0810.5362, 24 pp.
            This manuscript provides some supporting details for [11].

[12]  "Dynkin diagram classifications of posets satisfying certain structural properties"
          Preprint.

[13]  "Distributive lattices and Weyl characters for certain families of irreducible semisimple Lie algebra representations"
          With Norman Wildberger. In preparation.