# Decomposing Hessenberg varieties over classical groups

@article{Tymoczko2002DecomposingHV, title={Decomposing Hessenberg varieties over classical groups}, author={Julianna Tymoczko}, journal={arXiv: Algebraic Geometry}, year={2002} }

Hessenberg varieties are a family of subvarieties of the flag variety, including the Springer fibers, the Peterson variety, and the entire flag variety itself. The seminal example arises from a problem in numerical analysis and consists for a fixed linear operator M of the full flags V_1 \subsetneq V_2 >... \subsetneq V_n in GL_n with M V_i contained in V_{i+1} for all i.
In this paper I show that all Hessenberg varieties in type A_n and semisimple and regular nilpotent Hessenberg varieties in…

## 10 Citations

### Affine pavings of Hessenberg varieties for semisimple groups

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In this paper, we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. We prove that Hessenberg varieties corresponding to nilpotent elements which are regular in…

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This work is intended to contextualize and enhance certain well-studied relationships between Hessenberg varieties and the Toda lattice, thereby building on the results of Kostant, Peterson, and…

### Properties of singular schubert varieties

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### Multicontact mappings on Hessenberg manifolds

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This thesis was inspired by work of M. Cowling, F. De Mari, A. Koranyi and M. Reimann, who studied multicontact structures for the homogeneous manifolds G/P, where G is a semisimple Lie group and P…

### Hessenberg varieties for the minimal nilpotent orbit

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For a connected, simply-connected complex simple algebraic group $G$, we examine a class of Hessenberg varieties associated with the minimal nilpotent orbit. In particular, we compute the…

### Graham's variety and perverse sheaves on the nilpotent cone

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### Hessenberg varieties, Slodowy slices, and integrable systems

- Materials ScienceMathematische Zeitschrift
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This work is intended to contextualize and enhance certain well-studied relationships between Hessenberg varieties and the Toda lattice, thereby building on the results of Kostant, Peterson, and…

### Affine pavings of Hessenberg varieties for semisimple groups

- MathematicsSelecta Mathematica
- 2012

In this paper, we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. We prove that Hessenberg varieties corresponding to nilpotent elements which are regular in…

### Variations on a Theme of Schubert Calculus

- MathematicsAssociation for Women in Mathematics Series
- 2019

In this tutorial, we provide an overview of many of the established combinatorial and algebraic tools of Schubert calculus, the modern area of enumerative geometry that encapsulates a wide variety of…

### Exponents for B-stable ideals

- Mathematics
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Let G be a simple algebraic group over the complex numbers containing a Borel subgroup B. Given a B-stable ideal I in the nilradical of the Lie algebra of B, we define natural numbers m 1 , m 2 ,...,…

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