相关论文: The Canonical Component of the nilfibre for Parabo…

This work is a continuation of [Y. Fittouhi and A. Joseph, Weierstrass Sections for Parabolic adjoint action in type $A$]. Let $G$ be an irreducible simple algebraic group and $B$ a Borel subgroup of $G$. Let $\mathfrak n$ be the Lie…

A "Composition map" is constructed, leaning heavily on earlier work [Y. Fittouhi and A. Joseph, Parabolic adjoint action, Weierstrass sections and components of the nilfibre in type $A$, Indag Math. and Y. Fittouhi and A. Joseph, The…

The notion of "Weierstrass Section", comes from Weierstrass canonical form for elliptic curves. In celebrated work [B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327-404] constructed such a section for…

In this paper, using Bourbaki's convention, we consider a simple Lie algebra $\mathfrak g\subset\mathfrak g\mathfrak l_m$ of type B, C or D and a parabolic subalgebra $\mathfrak p$ of $\mathfrak g$ associated with a Levi factor composed…

Let $G$ be a simple algebraic group over the complex field $\mathbb C$, $P$ a parabolic subgroup containing $B$ its Borel subgroup, $P'$ its derived group and $\mathfrak m$ the Lie algebra of its nilradical. The nilfibre $\mathscr N$ for…

Adapted pairs and Weierstrass sections are central to the invariant theory associated to the action of an algebraic Lie algebra a on a finite dimensional vector space X. In this a need not be a semisimple Lie algebra. Here their general…

In the paper the algebra of invariants of the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra is studied. We set up a conjecture on the structure of the algebra of invariants. The conjecture is proved…

The flag variety of a complex reductive linear algebraic group G is by definition the quotient G/B by a Borel subgroup. It can be regarded as the set of Borel subalgebras of Lie(G). Given a nilpotent element e in Lie(G), one calls Springer…

We consider a proper parabolic subalgebra p of a simple Lie algebra g and the Inonu-Wigner contraction of p with respect to its decomposition into its standard Levi factor and its nilpotent radical : this is the Lie algebra which is…

In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated…

A linearized function field $F$ can be viewed as a Galois extension of a rational function field $K(x)$. For a totally ramified place $Q$ of degree one in $F/K(x)$, we give a unified description of the set $G(Q)$ of gaps at $Q$. As a…

Let G be either an orthogonal, a symplectic or a unitary group over a local field F and let P = MN be a maximal parabolic subgroup. Then the Levi subgroup M is the product of a group of the same type as G and a general linear group, acting…

The Weierstrass curve is a pointed curve $(X,\infty)$ with a numerical semigroup $H_X$, which is a normalization of the curve given by the Weierstrass canonical form, $y^r + A_{1}(x) y^{r-1} + A_{2}(x) y^{r-2} +\dots + A_{r-1}(x) y +…

We study invariants of the adjoint action of the unipotent group in the nilradical of a parabolic subalgebra of types Bn, Cn, Dn. We introduce the notion of expanded base in the set of positive roots and construct an invariant for every…

The {\it Weierstrass semigroup} of pole orders of meromorphic functions in a point $p$ of a smooth algebraic curve $C$ is a classical object of study; a celebrated problem of Hurwitz is to characterize which semigroups ${\rm S} \subset…

Let $G$ be a simple Lie group. Consider a nilpotent element $e\in \mathfrak{g}$. Let $Z_G(e)$ be the centralizer of $e$ in $G$, and let $A_e:= Z_G(e)/Z_G(e)^{o}$ be its component group. Write $\text{Irr}(\mathcal{B}_e)$ for the set of…

We show that the roots of a Weierstrass polynomial on several variables are power series with rational exponents of bounded denominators, whose Newton diagrams are contained in an S-cone. As an application, in Section 4 we deal with some…

Let $\mathfrak a$ be an algebraic Lie subalgebra of a simple Lie algebra $\mathfrak g$ with index $\mathfrak a \leq \rank \mathfrak g$. Let $Y(\mathfrak a)$ denote the algebra of $\mathfrak a$ invariant polynomial functions on $\mathfrak…

Let $K$ be an algebraically closed field with characteristic zero, and $\mathfrak{g}$ a Lie algebra. Let $Y(\mathfrak{g})$ be the subalgebra of the symmetric algebra $S(\mathfrak{g})=K[\mathfrak{g}^*]$ made of the polynomials which are…

Questions concerning small fractional parts of polynomials and pseudo-polynomials have a long history in analytic number theory. In this paper, we improve on earlier work by Madritsch and Tichy. In particular, let $f=P+\phi$ where $P$ is a…