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*(2*n*+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.

Dr. Robert G. DonnellyProfessor of Mathematics ## Department of Mathematics and Statistics |