The University of Michigan Combinatorics Seminar
Winter 2003
February 12, 3:10-4:00, 3866 East Hall



An introduction to Hessenberg varieties

Julianna Tymoczko

Princeton University




Abstract

Hessenberg varieties form a family of subvarieties of the flag variety with important relations to representation theory, numerical analysis, quantum cohomology, and other areas. Significant examples include the Springer fiber (whose cohomology carries information about representations of the Weyl group) and the Peterson variety (which can be stratified so that the open stratum's coordinate ring gives the quantum cohomology of the flag variety).

I will discuss the geometric structure of Hessenberg varieties and will describe how several major classes of Hessenberg varieties can be paved by affines. I will show how these affines are indexed by filled Young tableaux and how their dimensions can be computed by simple combinatorial rules.