Related papers: Parabolic subgroups and Automorphism groups of Sch…

In this paper are described the groups of automorphisms of semigroup End(W(X)), where W(X) is free commutative or free associative algebra.

Kostant constructed a section from the adjoint quotient morphism of a simple Lie algebra to the open set of regular elements, and Steinberg constructed such a section for the adjoint quotient of a simply connected and simple algebraic…

The action of a torus group $T$ on a symplectic toric manifold $(M,\omega)$ often extends to an effective action of a (non-abelian) compact Lie group $G$. We may think of $T$ and $G$ as compact Lie subgroups of the symplectomorphism group…

For a Weyl group $W$ of classical type, we present a formula to calculate the restriction of (graded) Springer representations of $W$ to a maximal parabolic subgroup $W'$ where the types of $W$ and $W'$ are in the same series. As a result,…

Given a connected reductive algebraic group $G$ and a Borel subgroup $B \subseteq G$, we study $B$-normalized one-parameter additive group actions on affine spherical $G$-varieties. We establish basic properties of such actions and their…

In arXiv:2011.03313, the author has constructed a category of abstractly automorphic representations for $\mathrm{GL}(2)$ over a function field $F$. This is a symmetric monoidal Abelian category, constructed with the goal of having the…

Let G be an algebraic reductive group over a an algebraically closed field of positive characteristic. Choose a parabolic subgroup $P$ in $G$ and denote by $U$ its unipotent radical. Let $X$ be a $G$-variety. The purpose of this paper is to…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

In this paper, we assume that $G$ is a finitely generated torsion free non-elementary Kleinian group with $\Omega(G)$ nonempty. We show that the maximal number of elements of $G$ that can be pinched is precisely the maximal number of rank 1…

Let $P$ be a parabolic subgroup in $G=SL_n(\mathbf k)$, for $\mathbf k$ an algebraically closed field. We show that there is a $G$-stable closed subvariety of an affine Schubert variety in an affine partial flag variety which is a natural…

In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple linear…

We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated to a rectangular element is indeed a Schubert variety in a partial flag…

Let $L_w$ be the Levi part of the stabilizer $Q_w$ in $GL_N$ (for left multiplication) of a Schubert variety $X(w)$ in the Grassmannian $G_{d,N}$. For the natural action of $L_w$ on $\mathbb{C}[X(w)]$, the homogeneous coordinate ring of…

Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy…

A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r} \mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its action on…

Let $\g$ be a locally reductive complex Lie algebra which admits a faithful countable-dimensional finitary representation $V$. Such a Lie algebra is a split extension of an abelian Lie algebra by a direct sum of copies of $\sl_\infty$,…

Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$…

Elaborating on a paper by Suter, we provide a detailed description of the automorphism group of the poset of abelian ideals in a Borel subalgebra of a finite dimensional complex simple Lie algebra.

The Schubert varieties on a flag manifold G/P give rise to a cell decomposition on G/P whose Kronecker duals, known as the Schubert classes on G/P, form an additive base of the integral cohomology of G/P. The Schubert's problem of…

Given a regular supercuspidal representation $\rho$ of the Levi subgroup $M$ of a standard parabolic subgroup $P=MN$ in a connected reductive group $G$ defined over a non-archimedean local field $F$, we serve you a Rodier type structure…