8 papers
Ideals defining components of two-row Springer fibers
Cristina Sabando-Alvarez, Martha Precup
Springer fibers are subvarieties of the flag variety parameterized by nilpotent matrices. They are central objects of study in geometry representation theory. This paper focuses on…
Hessenberg varieties of codimension one in the flag variety
Laura Escobar, Martha Precup, John Shareshian
We study geometric and topological properties of Hessenberg varieties of codimension one in the type A flag variety. Our main results: (1) give a formula for the Poincaré polynomi…
Restricted inversion polynomials
Jeongwon Lee, Nathan Lesnevich, Martha Precup
For a finite subset of positive integers, the descent polynomial counts the number of permutations in that have descent set . We generalize descent…
Richardson tableaux and components of Springer fibers equal to Richardson varieties
Steven N. Karp, Martha E. Precup
Motivated by the study of Springer fibers and their totally nonnegative counterparts, we define a new subset of standard tableaux called Richardson tableaux. We characterize Richar…
Perverse sheaves, nilpotent Hessenberg varieties, and the modular law
Martha Precup, Eric Sommers
We consider generalizations of the Springer resolution of the nilpotent cone of a simple Lie algebra by replacing the cotangent bundle with certain other vector bundles over the fl…
Matrix Hessenberg schemes over the minimal sheet
Rebecca Goldin, Martha Precup
We study families of matrix Hessenberg schemes in the affine scheme of complex matrices, each defined over a fixed sheet in the Lie algebra $\mathfrak{gl}_n(\mathbb{C})…