22 citations · 42 across the 19 of their papers we have counts for
26 papers
Restrictions of the dot action representation
Hsin-Chieh Liao, Martha Precup, John Shareshian
Regular semisimple Hessenberg varieties are subvarieties of flag varieties defined for any reductive group. Their cohomology carries a representation of the associated Weyl group,…
Dimensions of type Hessenberg varieties over a fixed sheet
Megumi Harada, Martha Precup, Colleen Robichaux
Hessenberg varieties are subvarieties of the flag variety parameterized by a Hessenberg function and a ma…
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…
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…
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})…
Regular Hessenberg varieties for the minimal indecomposable Hessenberg space
Erik Insko, Martha Precup, Alexander Woo
This paper investigates the geometry of regular Hessenberg varieties associated with the minimal indecomposable Hessenberg space in the flag variety of a complex reductive group. T…
Minimal semisimple Hessenberg schemes
Rebecca Goldin, Martha Precup
We study a collection of Hessenberg varieties in the type A flag variety associated to a nonzero semisimple matrix whose conjugacy class has minimal dimension. We prove each such m…
Geometric and combinatorial properties of extended Springer fibers
William Graham, Martha Precup, Amber Russell
We consider a generalization of the Springer resolution studied in earlier work of the authors, called the extended Springer resolution. In type , this map plays a role in Luszt…
-Orbit closures and Hessenberg varieties
Mahir Bilen Can, Martha Precup, John Shareshian +1
This article explores the relationship between Hessenberg varieties associated with semisimple operators with two eigenvalues and orbit closures of a spherical subgroup of the gene…
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 polynomia…
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…
Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties
Megumi Harada, Martha Precup
It is well-known that the -fixed points of a Schubert variety in the flag variety can be characterized purely combinatorially in terms of Bruhat order on th…
Which Schubert Varieties are Hessenberg Varieties?
Laura Escobar, Martha Precup, John Shareshian
After proving that every Schubert variety in the full flag variety of a complex reductive group is a general Hessenberg variety, we show that not all such Schubert varieties ar…
Toward permutation bases in the equivariant cohomology rings of regular semisimple Hessenberg varieties
Megumi Harada, Martha Precup, Julianna Tymoczko
Recent work of Shareshian and Wachs, Brosnan and Chow, and Guay-Paquet connects the well-known Stanley-Stembridge conjecture in combinatorics to the dot action of the symmetric gro…
A new approach to the generalized Springer correspondence
William Graham, Martha Precup, Amber Russell
The Springer resolution of the nilpotent cone is used to give a geometric construction of the irreducible representations of Weyl groups. Borho and MacPherson obtain the Springer c…
An equivariant basis for the cohomology of Springer fibers
Martha Precup, Edward Richmond
Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this paper, we analyze the equivariant coh…
Hessenberg varieties associated to ad-nilpotent ideals
Caleb Ji, Martha Precup
We consider Hessenberg varieties in the flag variety of with the property that the corresponding Hessenberg function defines an ad-nilpotent ideal. Each such Hes…
Upper-triangular linear relations on multiplicities and the Stanley-Stembridge conjecture
Megumi Harada, Martha Precup
In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in combinatorics to the geometry of…
The singular locus of semisimple Hessenberg varieties
Erik Insko, Martha Precup
Although regular semisimple Hessenberg varieties are smooth and irreducible, semisimple Hessenberg varieties are not necessarily smooth in general. In this paper we determine the i…
The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture
Megumi Harada, Martha Precup
We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson. We gi…
Hessenberg varieties of parabolic type
Martha Precup, Julianna Tymoczko
This paper studies the geometry and combinatorics of three interrelated varieties: Springer fibers, Steinberg varieties, and parabolic Hessenberg varieties. We prove that each para…
Springer fibers and Schubert points
Martha Precup, Julianna Tymoczko
Springer fibers are subvarieties of the flag variety parametrized by partitions; they are central objects of study in geometric representation theory. Schubert varieties are subvar…
The Betti numbers of regular Hessenberg varieties are palindromic
Martha Precup
Recently Brosnan and Chow have proven a conjecture of Shareshian and Wachs describing a representation of the symmetric group on the cohomology of regular semisimple Hessenberg var…