# Annette Pilkington

*Professor of the Practice*

## Education

B.A. (Hons) Mathematics and Economics, 1984

M.A. University College Dublin, Ireland, 1985

Ph.D., University of Notre Dame, 1991

## Research Group

Algebra and Algebraic Geometry

## Research Area

Algebra

## Bio

**Research Interests**

My research uses results from Classical groups, K-theory, Number theory, Quadratic forms, Coxeter groups and representation theory. In particular, with respect to classical groups, my work has focused on the theory of the group SL_2 over number rings and the behavior of its subgroups related to ideals in the rings. I am still interested in some unresolved questions from K-theory, concerning SL_2 over rings. More recently I have done some work on convex geometries on root systems related to Coxeter groups. I have compared several natural convex closure operators on these root systems, and considered the question as to when they satisfy an anti-exchange condition, defined by Edelamn and Jamison.

I am currently working on the representation theory of an interesting algebra related to the n by n matrices over the ring R $\otimes$ R, where R is the ring of integers of a number field. The representation theory can be explored using the results of Dyer on Category C, and has interesting connections with the number theory of the rings.

**Selected Publications**

- The E_2® – Normalized Subgroups of GL_2®: Journal of Algebra 172, 584-611 (1995).
- The E_2® – Normalized Subgroups of GL_2® II: Journal of Algebra 177, 619-626 (1995)
- The highest weight representations from number ring.: In preparation.
- Convex closures on root systems: Submitted for publication.

**Email:** apilking@nd.edu

**Phone:** 574-631-3369

**Fax:** 574-631-6579

**Office:** 232 Hayes-Healy Bldg