28 citations · 90 across the 19 of their papers we have counts for
4 papers · 1 filter
The equivariant cohomology rings of regular nilpotent Hessenberg varieties in Lie type A: a research announcement
Hiraku Abe, Megumi Harada, Tatsuya Horiguchi +1
Let be a fixed positive integer and a Hessenberg function. The main result of this manuscript is to give a systematic method for pr…
The torus equivariant cohomology rings of Springer varieties
Hiraku Abe, Tatsuya Horiguchi
The Springer variety of type associated to a nilpotent operator on in Jordan canonical form admits a natural action of the -dimensional torus wh…
Young diagrams and intersection numbers for toric manifolds associated with Weyl chambers
Hiraku Abe
We study intersection numbers of invariant divisors in the toric manifold associated with the fan determined by the collection of Weyl chambers for each root system of classical ty…
Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry
Hiraku Abe, Sara Billey
In 1990, Lakshmibai and Sandhya published a characterization of singular Schubert varieties in flag manifolds using the notion of pattern avoidance. This was the first time pattern…