William Monty McGovern
Professor, appointed 1990 (Ph.D. M.I.T. 1987)
Research area: Representation theory
E-mail: mcgovern[_a_t_]math.washington.edu
Phone: 543-1149
Office: PDL C-450
Office hours: TuTh/1:30pm or by appointment
Courses taught this quarter: MATH 326 A & 411 A
Hobbies: I play piano and English handbells and sing in a church choir.
Professional interests
I study the (algebraic) representation theory of Lie groups and Lie algebras; that is, the ways to realize, or represent, Lie groups or algebras as groups or algebras of matrices. Originally these matrices had finite size, as in linear algebra, but nowadays they usually have infinite size. I combine classical techniques from noncommutative ring theory with newer techniques from combinatorics to "tame" the infinite matrices, studying and understanding them in much the same way as the finite matrices were studied earlier. In more technical language, I study primitive ideals in enveloping algebras of semisimple Lie algebras; that is, annihilators of irreducible representations of such enveloping algebras.
In recent years I have gotten involved in some administrative work; I
served as chair of the Teaching Quality Committee in the department and as
a member of the university-wide Faculty Council on Instructional Quality.
Currently I serve as TA Coordinator for the department. I also help out
at my sons' elementary school, coaching their math team for a statewide
contest in Blaine in the spring.
Selected bibliography
Rings of regular functions on nilpotent orbits and their covers, Inv.
Math., 97 (1989), 209-217.
Completely prime maximal ideals and quantization, Mem. Amer. Math. Soc.,
519 (1994).
Cells of Harish-Chandra modules for real classical groups, Amer. J. Math.,
120 (1998), 211-227.
On the Spaltenstein-Steinberg map for classical Lie algebras, Comm. in Alg.,
27 (1999), 2979-2993.
A triangularity result for associated varieties of highest weight modules,
Comm. in Alg., 28 (2000), 1835-1843.