My work involves studying the properties of reductive algebraic groups. Algebraic groups are groups equipped with the Zariski topology such that the multiplication and inverse maps are maps of varieties. They behave like Lie groups, except that there is the freedom to work over any field. Specifically, I study the objects that arise when trying to understand the representation theory of algebraic groups, especially nilpotent orbits and affine Weyl groups. Recently I have been thinking about the connection between nilpotent orbits, Borel-stable ideals in the nilradical, Kazhdan-Lusztig cells, and certain duality maps.
No subject area
Exterior powers of the reflection representation in Springer theory, Mathematics and Statistics Department Faculty Publication Series (2010)
We give a proof of a conjecture of Lehrer and Shoji regarding the occurrences of...
Pieces of the nilpotent cones for classical groups (with Promad Achar and Anthony Henderson), Mathematics and Statistics Department Faculty Publication Series (2010)
We compare orbits in the nilpotent cone of type $B_n$, that of type $C_n$, and...
Cohomology of the line bundles on the contangent bundle of grassmannian, Proceedings of the American Mathematical Society (2009)
e show that certain line bundles on the cotangent bundle of a Grassmannian arising from...
Equivalence classes of ideals in the nilradical of a Borel subalgebra, Nagoya Mathematical Journal (2006)
An equivalence relation is defined and studied on the set of $B$-stable ideals in the...
Exponents for B-stable ideals (with J Tymoczko), Transaction of the American Mathematical Society (2006)
Let be a simple algebraic group over the complex numbers containing a Borel subgroup ....