Preprints and publications

"Gelfand-Graev characters of the finite unitary groups"

Joint with C.R. Vinroot. Gelfand-Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the language of symmetric functions, we study degenerate Gelfand-Graev characters of the finite unitary group from a combinatorial point of view. In particular, we give the values of Gelfand-Graev characters at arbitrary elements, recover the decomposition multiplicities of degenerate Gelfand-Graev characters in terms of tableau combinatorics, and conclude with some multiplicity consequences. pdf.

"Supercharacter formulas for pattern groups"

Joint with P. Diaconis. C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group U_n(F_q). In this theory superclasses are certain unions of conjugacy classes, and supercharacters are a set of characters which are constant on superclasses. This paper gives a character formula for a supercharacter evaluated at a superclass for pattern groups and more generally for algebra groups. .pdf .

"On the characteristic map of finite unitary groups''

Joint with C.R. Vinroot. This paper describes the analogue of Green's characteristic map for the unitary group, and gives some representation theoretic applications. To appear in Advances in Mathematics. pdf .

This paper extends the work of the paper below by analyzing the\ multiplication of basis elements in Unipotent Hecke algebras. This work is done in general type, but a section is devoted to working out the combinatorics in the general linear group case. To appear in Transactions of the American Mathematical Society. pdf .

This paper examines a family of Hecke algebras that generalize both the Iwahori-Hecke algebra and the Gelfand-Graev Hecke algebra. I give an explicit basis for these algebras, describe a Cartan-like subalgebra and allow the representation theory to inspire a generalization of the RSK correspondence. Journal of Algebra 284 (2005): 559-577.

This is my thesis pdf .

"Quadratic Corestriction, C_2-embedding problems, and explicit construction"

Joint with J. Swallow. This paper came out of an REU at Davidson College. We investigate aspects of the inverse Galois problem. Communications in Algebra 30 (2002): 3227-3258.