Randall R Holmes

Professor Emeritus
Department of Mathematics and Statistics
Auburn University, AL 36849

holmerr@auburn.edu

MATH 1617 Honors Calculus I
MATH 2660 Topics in Linear Algebra
MATH 3100 Intro to Advanced Mathematics
MATH 5310/6310 Intro to Abstract Algebra I
MATH 5320/6320 Intro to Abstract Algebra II
MATH 5500/6500 Intro to Topology
MATH 7310 Algebra I
MATH 7330 Linear Representations of Finite Groups
MATH 8310 Homological Algebra I
MATH 8320 Homological Algebra II
MATH 8970 Category Theory

Auburn University	Professor Emeritus	(2019-present)
Auburn University	Professor	(2007-2019)
Auburn University	Associate Professor	(1994-2007)
Auburn University	Assistant Professor	(1989-94)
Yale University	J. W. Gibbs Instructor	(1987-89)

Ph.D. Mathematics (1987), University of Illinois-Urbana, Advisor: Professor Michio Suzuki.
M.A. Mathematics (1982), University of Missouri-Columbia.
Three years of study in music composition (1978-81), University of Missouri-Columbia.
B.S. Education (Mathematics and Physics) (1978), University of Missouri-Columbia.

(Links are to preprints)

Simplicity of Kac modules for the quantum general linear superalgebra (with C. Zhang), Algebr. Represent. Theory (2019), to appear.
Symmetry classes of tensors associated with principal indecomposable characters and Osima idempotents (with A. Kodithuwakku), Lin. Multilinear Alg. 64 (2016), no. 4, 574—586.
Geometry of standard symmetrized tensors (with H. Harmon), Linear Algebra and Its Applications 460 (2014), 136—150.
Orthogonal bases of Brauer symmetry classes of tensors for the dihedral group (with A. Kodithuwakku), Linear Multilinear Algebra 61(8) (2013), 1136—1147.
The coefficient coalgebra of a symmetrized tensor space (with D. Turner), Linear Multilinear Algebra 60(4) (2012), 385—396.
Asymptotic behavior of Iwasawa and Cholesky iterations (with H. Huang and T.-Y. Tam), Linear Algebra and Its Applications 438, no. 10 (2011), 3755—3768.
Population inertia and its sensitivity to changes in vital rates or initial conditions (with D. N. Koons and J. B. Grand), Ecology 88 (2007), 2857—2867.
Temporal and latitudinal variation in Northern Bobwhite population dynamics (with T. H. Folk and J. B. Grand), Population Ecology 49(3) (2007), 211—219.
Group Representations (with T.-Y. Tam), chapter in CRC Handbook of Linear Algebra (2006), 68-1—11.
Simple modules for the restricted Cartan type Lie algebras (with C. Zhang), Algebr. Represent. Theory 9, no. 3 (2006), 285—307.
Numerical Range of the Derivation of an Induced Operator (with C. K. Li and T.-Y. Tam), J. Austral. Math. Soc. (Series A) 82(3) (2005), 325—343.
Orthogonality of cosets relative to irreducible characters of finite groups , Linear Multilinear Algebra 52, no. 2 (2004), 133—143.
A generalization of the Deutsch-Jozsa quantum algorithm (with F. Texier), Far East J. Math. Sci. (FJMS) 9, no. 3 (2003), 319—326.
Some simple modules for the restricted Cartan-type Lie Algebras (with C. Zhang), J. Pure Appl. Algebra 173, no. 2 (2002), 135—165.
Simple modules with character height at most one for the restricted Witt algebras , J. Algebra 237, no. 2 (2001), 446—469.
Distance to the convex hull of an orbit under the action of a compact Lie group (with T.-Y. Tam), J. Austral. Math. Soc. Ser. A 66, no. 3 (1999), 331—357.
Simple restricted modules for the restricted Hamiltonian algebra , J. Algebra 199, no. 1 (1998), 229—261.
Orthogonal bases of symmetrized tensor spaces , Linear Multilinear Algebra 39, no. 3 (1995), 241—243.
A duality proof of a theorem of P. Hill , Proc. Amer. Math. Soc. 123, no. 2 (1995), 351—353.
Dimensions of the simple restricted modules for the restricted contact Lie algebra , J. Algebra 170, no. 2 (1994), 504—525.
Cartan invariants for the restricted toral rank two contact Lie algebra , Indag. Math. (N.S.) 5, no. 3 (1994), 291—305.
Block degeneracy and Cartan invariants for graded Lie algebras of Cartan type (with D. Nakano), J. Algebra 161, no. 1 (1993), 155—170.
Symmetry classes of tensors associated with certain groups (with T.-Y. Tam), Linear Multilinear Algebra 32, no. 1 (1992), 21—31.
An algorithm for the projective characters of finite Chevalley groups , Rocky Mountain J. Math. 22, no. 2 (1992), 611—630.
Simple restricted modules for the restricted contact Lie algebras , Proc. Amer. Math. Soc. 116, no. 2 (1992), 329—337.
Brauer-type reciprocity for a class of graded associative algebras (with D. Nakano), J. Algebra 144, no. 1 (1991), 117—126.
Projective characters of finite Chevalley groups , J. Algebra 124, no. 1(1989), 158—182.

Randall R Holmes

Courses taught

Experience

Education

Selected publications