Related papers: Simple Modules of Classical Linear Groups with Nor…

We study GKZ-type D-modules arising from the actions of commutative linear algebraic groups G = TU (where T is a torus and U is unipotent) on a vector space. Building on Hotta's equivariant D-module framework, we formalize a Fourier-orbit…

We explore connected affine algebraic groups $G$, which enjoy the following finiteness property $\rm (F)$: for every algebraic action of $G$, the closure of every $G$-orbit contains only finitely many $G$-orbits. We obtain two main results.…

Let $\G$ be a semisimple algebraic group over a number field $K$, $\mathcal{S}$ a finite set of places of $K$, $K_\mathcal{S}$ the direct product of the completions $K_v, v \in \mathcal{S}$, and $\OO$ the ring of $\mathcal{S}$-integers of…

We classify all simple $W_n$-modules with finite-dimensional weight spaces. Every such module is either of a highest weight type or is a quotient of a module of tensor fields on a torus, which was conjectured by Eswara Rao. This generalizes…

Let $G$ be a simple simply connected algebraic group over an algebraically closed field $k$ of characteristic $p$, with $r$-th Frobenius kernel $G_r$. Let $M$ be a $G_r$-module and $V$ a rational $G$-module. We put a variety structure on…

Let $V$ be a finite-dimensional vector space over a finite field, and suppose $G \leq \Gamma \mathrm{L}(V)$ is a group with a unique subnormal quasisimple subgroup $E(G)$ that is absolutely irreducible on $V$. A base for $G$ is a set of…

We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient…

Let $X$ be a smooth affine algebraic variety over the field of complex numbers which is contractible. Then every algebraic $G$-torsor on $X$ is algebraically trivial if $G$ is a semi-simple algebraic group. We also show that if $X$ is a…

Let G be a connected simply-connected reductive algebraic group. In this article, we consider the normal algebraic varieties equipped with a horospherical G-action such that the quotient of a G-stable open subset is a curve. Let X be such a…

Let G be a connected linear algebraic group over a field k. We say that G is toric-friendly if for any field extension K/k and any maximal K-torus T in G the group G(K) has only one orbit in (G/T)(K). Our main result is a classification of…

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is…

We show that the orbit closures for directing modules over tame algebras are normal and Cohen-Macaulay. The proof is based on deformations to normal toric varieties.

Let $M$ be a smooth complex projective toric variety equipped with an action of a torus $T$, such that the complement $D$ of the open $T$--orbit in $M$ is a simple normal crossing divisor. Let $G$ be a complex reductive affine algebraic…

Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a Bruhat-Tits group scheme on $X$ which is generically semi-simple and trivial. We show that the \'etale fundamental group of the moduli stack…

We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.

It is known that for the natural algebraic torus actions on the Grassmannians, the closures of torus orbits are toric varieties, and that these toric varieties are smooth if and only if the corresponding matroid polytopes are simple. We…

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of…

The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular the following results are proved: a) If L is an algebraic subgroup of a connected real algebraic group G such that…

This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m,n in (1/T)Z_+, an A_{g,n}(V)-A_{g,m}(V)-bimodule A_{g,n,m}(V) is…

A regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient conditions under which a rational vertex…