Related papers: Codimensions of root valuation strata
This paper generalizes the classical theory of Newton polygons from the case of general linear groups to the case of split reductive groups. It also gives a root-theoretic formula for dimensions of Newton strata in the adjoint quotients of…
Let $k$ be an algebraically closed field and $G$ a connected reductive group over $k((t))$ satisfying some conditions. We define a stratification by conjugacy classes of twisted Levi subgroups of $G$ on each Moy-Prasad quotient…
We study the Newton stratification of the adjoint quotient of a connected split reductive group G with simply connected derived group over the field F of formal Laurent series in one variable over the field of complex numbers. Our main…
Splint of root system of simple Lie algebra appears naturally in the study of (regular) embeddings of reductive subalgebras. It can be used to derive branching rules. Application of splint properties drastically simplifies calculations of…
We study singular hyperkahler quotients of the cotangent bundle of a complex semisimple Lie group as stratified spaces whose strata are hyperkahler. We focus on one particular case where the stratification satisfies the frontier condition…
We study the possibility of factoring a covariant distribution on reductive Lie algebras as finite sum of products of an invariant distribution by a covariant polynomial.
Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint…
In this work we introduce the category of multiplicative sections of an $\la$-groupoid. We prove that this category carries natural strict Lie 2-algebra structures, which are Morita invariant. As applications, we study the algebraic…
We establish dimension formulas for the Witt vector affine Springer fibers associated to a reductive group over a mixed characteristic local field, under the assumption that the group is essentially tamely ramified and the residue…
Given a finite cocommutative Hopf algebra $A$ over a commutative regular ring $R$, the lattice of localising tensor ideals of the stable category of Gorenstein projective $A$-modules is described in terms of the corresponding lattices for…
The aim of this paper is to study relations between regular reductive PVs with one-dimensional scalar multiplication and the structure of graded Lie algebras. We will show that the regularity of such PVs is described by an…
We consider the family of polynomials $P(x,a)=x^n+a_1x^{n-1}+... +a_n$, $x,a_i\in {\bf R}$, and the stratification of ${\bf R}^n\cong \{(a_1,... ,a_n)|a_i\in {\bf R}\}$ defined by the multiplicity vector of the real roots of $P$. We prove…
In recent years, Benson, Iyengar and Krause have developed a theory of stratification for compactly generated triangulated categories with an action of a graded commutative Noetherian ring. Stratification implies a classification of…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a left-invariant path distance that is…
In this work, we refine recent results on the explicit construction of polynomial algebras associated with commutants of subalgebras in enveloping algebras of Lie algebras by considering an additional grading with respect to the subalgebra.…
We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…
The Z-grading determined by a long simple root of an affine or finite type Lie algebra arises from an adjoint or cominuscule representation of a lower rank semi-simple complex Lie algebra. Analysis of the relationship between the grading…
In the theory of so called "Covariant Quantum Mechanics" a basic role is played by Hermitian vector fields on a complex line bundle in the frameworks of Galilei and Einstein spacetimes. In fact, it has been proved that the Lie algebra of…
We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in…