相关论文: Geometric and unipotent crystals

Graded Hecke algebras can be constructed geometrically, with constructible sheaves and equivariant cohomology. The input consists of a complex reductive group G (possibly disconnected) and a cuspidal local system on a nilpotent orbit for a…

If a geometry $\Gamma$ is isomorphic to the residue of a point $A$ of a shadow geometry of a spherical building $\Delta$, a representation $\varepsilon_\Delta^A$ of $\Gamma$ can be given in the unipotent radical $U_{A^*}$ of the stabilizer…

Let $V$ be a finite-dimensional unitary representation of a compact quantum group $\mathrm{G}$ and denote by $\mathrm{G}_W$ the isotropy subgroup of a linear subspace $W\le V$ regarded as a point in the Grassmannian $\mathbb{G}(V)$. We show…

Suppose given a Hamiltonian and holomorphic action of $G=U(2)$ on a compact K\"{a}hler manifold $M$, with nowhere vanishing moment map. Given an integral coadjoint orbit $\mathcal{O}$ for $G$, under transversality assumptions we shall…

Let $A$ be a commutative algebra equipped with an action of a group $G$. The so-called $G$-primes of $A$ are the equivariant analogs of prime ideals, and of central importance in equivariant commutative algebra. When $G$ is an infinite…

The main theorem is that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X x S^n for any n greater than or equal to the…

Let $\mathcal{U}$ be the unipotent variety of a complex reductive group $G$. Fix opposed Borel subgroups $B_\pm \subseteq G$ with unipotent radicals $U_\pm$. The map that sends $x_+x_- \mapsto x_+x_-x_+^{-1}$ for all $x_\pm \in U_\pm$…

We consider (iced) quiver with potential $(\bar{Q}(D), F(D), \bar{W}(D))$ associated to a Postnilov Diagram $D$ and prove the mutation of the quiver with potential $(\bare{Q}(D), F(D), \bar{W}(D))$ is compatible with the geometric exchange…

We introduce the general notions of an overconvergent site and a constructible crystal on an overconvergent site. We show that if $V$ is a geometric materialization of a locally noetherian formal scheme $X$ over an analytic space $O$…

Suppose that we have a semisimple, connected, simply connected algebraic group $G$ with corresponding Lie algebra $\mathfrak{g}$. There is a Hopf pairing between the universal enveloping algebra $U(\mathfrak{g})$ and the coordinate ring…

Let G be a split, simple, simply connected, algebraic group over Q. The degree 4, weight 2 motivic cohomology group of the classifying space BG of G is identified with Z. We construct cocycles representing the generator of this group, known…

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,…

Let $\mathbb{G}$ be a split connected reductive group scheme over the ring of integers $\mathfrak{o}$ of a finite extension $L|\mathbb{Q}_p$ and $\lambda\in X(\mathbb{T})$ an algebraic character of a split maximal torus…

This is a sequel to \cite{osy} and \cite{sxy}. Associated with $G:=\GL_n$ and its rational representation $(\rho, M)$ over an algebraically closed filed $\bk$, we define an enhanced algebraic group $\uG:=G\ltimes_\rho M$ which is a product…

Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the…

Given a simple connected compact Lie group $K$ and a maximal torus $T$ of $K$, the Weyl group $W=N_K(T)/T$ naturally acts on $T$. First, we use the combinatorics of the (extended) affine Weyl group to provide an explicit $W$-equivariant…

The various types of compactifications of symmetric spaces and locally symmetric spaces are well-studied. Among them, the De Concini-Procesi compactification, also known as the wonderful compactification, of symmetric varieties has been…

We construct the crystalline fundamental group of a semi-stable variety over a field of positive characteristic using the log De Rham-Witt complex and Navarro-Aznar's derived Thom-Whitney functor. This approach gives a relatively direct…

In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety $\Zl$ in a quiver variety, and show the following results: (1) The…

Given a strict partial order $\Delta$ on a set $\Lambda$ and an arbitrary ring $R$ with $1\neq 0$, the corresponding McLain group $M(\Delta)$ has been studied in depth. We construct a larger family of McLain groups $G(\Delta)$, where…