Related papers: A note on Hessenberg varieties
We complete the determination of the generalised Springer correspondence for connected reductive algebraic groups, by proving a conjecture of Lusztig on the last open cases which occur for groups of type $E_8$.
In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail…
We prove a derived equivalence between each block of the derived category of sheaves on the nilpotent cone and the category of differential graded modules over a degeneration of Lusztig's graded Hecke algebra. Along the way, we construct…
We give a criterion which determines when a union of one-dimensional Deligne-Lusztig varieties has a connected closure. We also obtain a new, short proof of the connectedness criterion for Deligne-Lusztig varieties due to Lusztig.
In this paper we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. We give a connectedness criterion for semisimple Hessenberg varieties generalizing a criterion given by Anderson and Tymoczko. We show…
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot-action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In type A,…
We prove several Stern's type congruences for generalized bernoulli numbers.
We give a combinatorial description of the Springer correspondence for classical Lie algebras $\mathfrak{g}$ of type $B,C$ or $D$ and their duals $\mathfrak{g}^*$ in characteristic 2. The combinatorics used here is of the same kind as those…
We close a gap in the explicit determination of the generalized Springer correspondence for a connected reductive group in good characteristic.
The Springer variety is the set of flags stabilized by a nilpotent operator. In 1976, T.A. Springer observed that this variety's cohomology ring carries a symmetric group action, and he offered a deep geometric construction of this action.…
We summarize results concerning the Bernstein property of differential equations.
In this paper, we prove a conjecture of Schnell in the surface case.
Given a semisimple complex linear algebraic group $G$ and a lower ideal $I$ in positive roots of $G$, three objects arise: the ideal arrangement $\mathcal{A}_I$, the regular nilpotent Hessenberg variety $\mbox{Hess}(N,I)$, and the regular…
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
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 varieties for $GL_n(\mathbb{C})$. A key component of their…
For any connected complex reductive group $G$ and element $z$ of its Weyl group $W$, we use work of Lusztig and Abreu-Nigro to compute the graded $W$-character of the intersection cohomology of any closed Lusztig variety for $z$ over the…
As an extension of an author's previous paper, we prove the Gersten-type conjecture for the mod $p$ \'{e}tale motivic cohomology over a local ring of mixed characteristic $(0, p)$. We also prove the $\mathbb{P}^{1}$-homotopy invariance for…
We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related…
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 give an inductive formula for the $S_n$-representation on the…
In this paper we establish Springer correspondence for the symmetric pair $(\mathrm{SL}(N),\mathrm{SO}(N))$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaves construction due to Grinberg. As applications, we…