The Cohomology Rings of Regular Nilpotent Hessenberg Varieties in Lie Type A
نویسندگان
چکیده
منابع مشابه
Decomposing Nilpotent Hessenberg Varieties over Classical Groups
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 numerical analysis and consists, for a fixed linear operator M , of the full flags V1 ( V2 . . . ( Vn in GLn with MVi ⊆ Vi+1 for all i. In this paper, I show that all nilpotent Hessenberg varieties in type...
متن کاملUnit Interval Orders and the Dot Action on the Cohomology of Regular Semisimple Hessenberg Varieties
Motivated by a 1993 conjecture of Stanley and Stembridge, Shareshian and Wachs conjectured that the characteristic map takes the dot action of the symmetric group on the cohomology of a regular semisimple Hessenberg variety to ωXG(t), where XG(t) is the chromatic quasisymmetric function of the incomparability graph G of the corresponding natural unit interval order, and ω is the usual involutio...
متن کاملnilpotent quotients in finitely presented Lie rings †
A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...
متن کاملsecond cohomology of lie rings and the schur multiplier
we exhibit an explicit construction for the second cohomology group $h^2(l, a)$ for a lie ring $l$ and a trivial $l$-module $a$. we show how the elements of $h^2(l, a)$ correspond one-to-one to the equivalence classes of central extensions of $l$ by $a$, where $a$ now is considered as an abelian lie ring. for a finite lie ring $l$ we also show that $h^2(l, c^*) cong m(l)$...
متن کاملOn the Structure of the Cohomology of Nilpotent Lie Algebras
The exterior algebra over the centre of a Lie algebra acts on the cohomology of the Lie algebra in a natural way. Focusing on nilpotent Lie algebras, we explore the module structure afforded by this action. We show that for all two-step nilpotent Lie algebras, this module structure is non-trivial, which partially answers a conjecture of Cairns and Jessup [4]. The presence of free submodules ind...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2017
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnx275