Related papers: Unipotent Elements and Twisting in Link Homology

Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$. We show that if $G$ is nilpotent, then the…

Exploiting symmetry in Groebner basis computations is difficult when the symmetry takes the form of a group acting by automorphisms on monomials in finitely many variables. This is largely due to the fact that the group elements, being…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

We identify the equivariant coinvariant ring of a pseudo-reflection group with its image under the localization map. We then show that this image can be realized as the equivariant cohomology of a sort linear hypergraph, analogous to a GKM…

In this paper we study homological stability for spaces ${\rm Hom}(\mathbb{Z}^n,G)$ of pairwise commuting $n$-tuples in a Lie group $G$. We prove that for each $n\geqslant 1$, these spaces satisfy rational homological stability as $G$…

Consider a pair of $S$-dual hyperspherical varieties $G\circlearrowright X$ and $G^\vee\circlearrowright X^\vee$ equipped with equivariant quantizations $Q(X)$, $Q(X^\vee)$. Assume that the local conjecture of Ben-Zvi, Sakellaridis and…

We associate a bivariant theory to any suitable oriented Borel-Moore homology theory on the category of algebraic schemes or the category of algebraic G-schemes. Applying this to the theory of algebraic cobordism yields operational…

Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial,…

A periodic link, is link in $S^3$ with action of $\mathbb{Z}_p$ by rotation with $2\pi/p$ around a fixed unknot $U$. The equivariant Khovanov homology of periodic links has been studied in \cite{BP17}. We prove that the equivariant Khovanov…

Let $G$ be a linear algebraic group over an algebraically closed field of characteristic $p\geq 0$. We show that if $H_1$ and $H_2$ are connected subgroups of $G$ such that $H_1$ and $H_2$ have a common maximal unipotent subgroup and…

Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that a compact and connected Lie group $G$ acts on $M$ in a Hamiltonian manner, and that this action linearizes to $A$. Then there is an associated unitary…

The uniform $\mathcal{F}_p$-isomorphism theorem of Quillen gives a comparison map between the Borel equivariant $\mathbf{Z}/p$-cohomology of a space and a limit involving only the Borel equivariant cohomology groups of the same space with…

We define a homology $\mathcal{H}_N$ for closed braids by applying Khovanov and Rozansky's matrix factorization construction with potential $ax^{N+1}$. Up to a grading shift, $\mathcal{H}_0$ is the HOMFLYPT homology defined in…

Using equivariant obstruction theory we construct equivariant maps from certain classifying spaces to representation spheres for cyclic groups, product of elementary Abelian groups and dihedral groups. Restricting them to finite skeleta…

A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of…

Let $G$ a semisimple Lie group of non-compact type and let $\mathcal{X}_G$ be the Riemannian symmetric space associated to it. Suppose $\mathcal{X}_G$ has dimension $n$ and it has no factor isometric to either $\mathbb{H}^2$ or…

The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invariants are notoriously difficult to find and often involve…

We give an explicit (new) morphism of modules between $H^*_T(G/P) \otimes H^*_T(P/B)$ and $H^*_T(G/B)$ and prove (the known result) that the two modules are isomorphic. Our map identifies submodules of the cohomology of the flag variety…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

Let G be a complex reductive algebraic group (not necessarily connected), let K be a maximal compact subgroup, and let A be a finitely generated Abelian group. We prove that the conjugation orbit space Hom(A,K)/K is a strong deformation…