Steven Glenn Jackson

I am an assistant professor in the Mathematics Department of the University of Massachusetts in Boston, and hold a Ph.D. in mathematics from Yale University. I am also a member of the American Mathematical Society, the Mathematical Association of America, and the Mathematicians and Education Reform Forum, and a National Project NeXT Fellow.

Research:

My research interests include invariant theory and representation theory. I am particularly interested in toric degenerations of categorical quotients of flag varieties and their use in the calculation of branching multiplicities. Recently I have also been working with Alfred Noël on some problems connected with prehomogeneous spaces of Dynkin-Kostant type arising in the theory of nilpotent orbits in real reductive Lie algebras. We are honored to have received the College of Science and Mathematics Outstanding Achievement Award for Research and Scholarship for this work.

Publications:

Prehomogeneous spaces associated with complex nilpotent orbits, with A. Noël, Journal of Algebra 289(2005), pp. 515--557. A computation of isotypic decompositions and relative invariants of prehomogeneous spaces of Dynkin-Kostant type arising from conjugacy classes of nilpotent elements in complex reductive Lie algebras.
A LiE subroutine for computing prehomogeneous spaces associated with complex nilpotent orbits, with A. Noël, Lecture Notes in Computer Science 3516(2005), pp. 611--618. An algorithm for determination of highest weights in prehomogeneous spaces of Dynkin-Kostant type, implemented in the computer algebra system LiE.
A LiE subroutine for computing prehomogeneous spaces associated with real nilpotent orbits, with A. Noël, Lecture Notes in Computer Science 3482(2005), pp. 512--521. An algorithm for determination of highest weights in prehomogeneous spaces arising via the Kostant-Sekiguchi correspondence from nilpotent orbits in simple real Lie algebras of inner type.
Prehomogeneous spaces associated with nilpotent orbits in simple real Lie algebras E₆₍₆₎ and E_6(-26), with A. Noël. Algorithmic determination of isotypic decompositions for exceptional simple real Lie algebras of non-inner type. (To appear in Experimental Mathematics.)
Prehomogeneous spaces associated with real nilpotent orbits, with A. Noël, Journal of Algebra 305(2006), pp. 194--269. An extension of our calculation of isotypic decompositions and relative invariants to prehomogeneous spaces arising via the Kostant-Sekiguchi correspondence from nilpotent orbits in real reductive Lie algebras.
Polarizable theta-stable parabolic subalgebras and KC -saturation in the non-compact real forms of G2 and F4, with A. Noël. An algorithm for computation of the KC-saturation of the nilradical of a polarizable theta-stable parabolic. (Submitted.)

Work in Progress:

Conormality of nilpotent orbits in classical Lie Algebras, with Hervé Sabourin. Classification of nilpotent orbits possessing transverse Poisson structures.
Conormality of nilpotent orbits in exceptional Lie Algebras, with Alfred Noël. Computer algebra project to find transverse Poisson structures in exceptional algebras.
K-spherical flag varieties and multiplicity-free branching rules. An explicit determination of covariant algebras for certain affine spherical cones, leading to combinatorial (positive-sum) branching rules for the corresponding symmetric pairs.
Toric degeneration of branching algebras, with R. Howe, S. Lee, E. Tan, and J. Willenbring. Construction of canonical bases for symmetric pair branching algebras, leading to equivariant degeneration of branching varieties to affine toric varieties.
Simplicial decomposition of restricted Littlewood-Richardson cones, with S. Kim. Generators and relations for toric degenerations of restricted-depth GLn tensor product varieties.
A geometric proof of the Newell-Littlewood rule. A proof that certain products of classical nullcones admit flat equivariant deformations to products of a single nullcone and an affine space, leading to simple proof of the Newell-Littlewood rule governing decomposition of the corresponding classical tensor products.

Classes:

Currently (spring 2008) I am teaching:

Math 480 (Special Topics: General Topology).

Contact Information:

Steven Glenn Jackson
Department of Mathematics
University of Massachusetts
100 Morrissey Boulevard
Boston, MA 02125-3393

Tel.: (617) 287-6469
Fax: (617) 287-6433
E-mail: jackson@math.umb.edu
Office: Sci-3-082
Office hours (spring 2008): Mondays 4:00 p.m.-5:00 p.m. and Wednesdays 2:30 p.m.-3:30 p.m.., or by appointment.

Calendar:

If you would like to make an appointment with me, please consult my calendar, find a free time, then e-mail me to claim it.