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Totally nonnegative Peterson variety and strongly dominant weight polytope
Hiraku Abe, Tao Gui, Haozhi Zeng
We study the totally nonnegative part of the Peterson variety in arbitrary Lie type and establish its connection to the strongly dominant weight polytope. In particular, we prove t…
Notes on the cohomology of partial Hessenberg varieties
Tatsuya Horiguchi, Mikiya Masuda, Takashi Sato +1
Hessenberg varieties are a family of subvarieties of full flag varieties. This family contains well-known varieties such as Springer fibers, Peterson varieties, and permutohedral v…
Automorphisms of GKM graphs and regular semisimple Hessenberg varieties
Donghoon Jang, Shintarô Kuroki, Mikiya Masuda +2
A regular semisimple Hessenberg variety is a smooth subvariety of the full flag variety associated with a regular semisimple matrix…
Totally nonnegative part of the Peterson variety in Lie type A
Hiraku Abe, Haozhi Zeng
The Peterson variety (which we denote by ) is a subvariety of the flag variety, introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag vari…
Peterson varieties and toric orbifolds associated to Cartan matrices
Hiraku Abe, Haozhi Zeng
The Peterson variety is a remarkable variety introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag varieties. The rational cohomology ring of…
The integral cohomology rings of Peterson varieties in type A
Hiraku Abe, Haozhi Zeng
In this paper, we study the ring structure of the integral cohomology of the Peterson variety of type . We give two kinds of descriptions: (1) we show that it is is…