• Corpus ID: 235727702

Permutation module decomposition of the second cohomology of a regular semisimple Hessenberg variety

@inproceedings{Cho2021PermutationMD,
  title={Permutation module decomposition of the second cohomology of a regular semisimple Hessenberg variety},
  author={Soojin Cho and Jaehyun Hong and Eunjeong Lee},
  year={2021}
}
. Regular semisimple Hessenberg varieties admit actions of associated Weyl groups on their cohomology spaces of each degree. In this paper, we consider the module structure of the cohomology spaces of regular semisimple Hessenberg varieties of type A . We define a subset of the Bia lynicki-Birula basis of the cohomology space which becomes a module generator set of the cohomology module of each degree. We use these generators to construct permutation submodules of the degree two cohomology… 

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References

SHOWING 1-10 OF 21 REFERENCES

Chromatic quasisymmetric functions

e-positivity of the coefficient of t in xgptq, http://timothychow.net/h2.pdf

  • [Online; accessed July
  • 2021

Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties

We consider bases for the cohomology space of regular semisimple Hessenberg varieties, consisting of the classes that naturally arise from the Bialynicki-Birula decomposition of the Hessenberg

Permutation actions on equivariant cohomology of flag varieties

  • Toric topology, Contemp. Math.,
  • 2008

A Symmetric Function Generalization of the Chromatic Polynomial of a Graph

Abstract For a finite graph G with d vertices we define a homogeneous symmetric function XG of degree d in the variables x1, x2, ... . If we set x1 = ... = xn= 1 and all other xi = 0, then we obtain

Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix

Let A∈gl(n, C) and let p be a positive integer. The Hessenberg variety of degree p for A is the subvariety Hess(p, A) of the complete flag manifold consisting of those flags S1⊂⋯⊂Sn−1in ℂn which

Singular Loci of Schubert Varieties

This text presents topics in a systematic fashion to engage a wide readership. It includes: generalities on G/B and G/Q; the Grassmannian and the flag variety SL_n/B' the tangent space and

On e-Positivity and e-Unimodality of Chromatic Quasi-symmetric Functions

TLDR
The work resolves Stanley's conjecture on chromatic symmetric functions of $(3+1)$-free posets for two classes of natural unit interval orders.

Permutation groups

The cohomology rings of regular nilpotent Hessenberg varieties in Lie type A

Let $n$ be a fixed positive integer and $h: \{1,2,\ldots,n\} \rightarrow \{1,2,\ldots,n\}$ a Hessenberg function. The main results of this paper are twofold. First, we give a systematic method,