共查询到20条相似文献,搜索用时 46 毫秒
1.
The Springer correspondence is a map from the set of unipotent conjugacy classes of a reductive algebraic group to the set of irreducible complex characters of the Weyl group. Here, we determine this map explicitly in the case of disconnected classical algebraic groups.
Mathematics Subject Classification (2000): Primary 20G05; Secondary 20C33. 相似文献
2.
G. CARNOVALE 《Transformation Groups》2012,17(3):615-637
Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let ?? be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical ??-twisted conjugacy classes are precisely those intersecting only Bruhat cells corresponding to twisted involutions in the Weyl group. We show how the analogue of this statement fails in the triality case. As a byproduct, we obtain a dimension formula for spherical twisted conjugacy classes that was originally obtained by J.-H. Lu in characteristic zero. 相似文献
3.
George Lusztig 《Transformation Groups》1996,1(1-2):83-97
We define a map from an affine Weyl group to the set of conjugacy classes of an ordinary Weyl group.
Supported in part by the National Science Foundation. 相似文献
4.
Let Uε(g) be the simply connected quantized enveloping
algebra at roots of one associated to a finite
dimensional complex simple Lie algebra g.
The De Concini-Kac-Procesi conjecture on the
dimension of the irreducible representations of Uε(g)
is proved for the representations corresponding to the
spherical conjugacy classes of the simply connected
algebraic group G with Lie algebra g. We
achieve this result by means of a new characterization
of the spherical conjugacy classes of G in terms of
elements of the Weyl group. 相似文献
5.
《Indagationes Mathematicae》2021,32(6):1240-1274
We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpotent orbits. We show that this map is the same as the one defined by Lusztig in Lfromto, (2011) and that the Kazhdan–Lusztig map in Kazhdan and Lusztig, (1998) is a section of our map. This settles several conjectures in the literature. For classical groups, we prove more refined results by introducing and studying the “skeleta” of affine Springer fibers. 相似文献
6.
J. E. Humphreys 《代数通讯》2013,41(6):475-490
With a Weyl group W and a positive integer p are associated p-linkage classes of weights [4,13]. Small deformations of such classes by elements of W are introduced here. These lead in turn to certain polynomials in p with highest term pm, m = number of positive roots (one polynomial for each conjugacy class of W), which are written down explicitly for types A1, A2, B2. These polynomials give (for each prime p) the degrees of the various large series of irreducible characters of the corresponding Chevalley group over the field of p elements. Indeed, the formal behavior of weights appears to reflect the actual behavior of the characters under reduction modulo p. 相似文献
7.
We study the space of Iwahori subalgebras containing a given element of a semisimple Lie algebra over C((ɛ)). We also define
and study a map from nilpotent orbits in a semisimple Lie algebra over C to conjugacy classes in the Weyl group.
Both authors were supported in part by the National Science Foundation. 相似文献
8.
Summary Letk be an infinite field of characteristic not equal to 2, 3, 5. In this paper, we construct a natural map from the set of orbits of certain prehomogeneous vector spaces to the set of isomorphism classes of Galois extensions ofk which are splitting fields of equations of certain degrees, and prove that the inverse image of this map corresponds bijectively with conjugacy classes of Galois homomorphisms.Oblatum 24-I-1992 & 23-IV-1992Both authors are supported by NSF Grant DMS-8803085, DMS-9101091; The first author was partially supported by NSA grant MDA904-91-H-0041 相似文献
9.
We show that for certain classes of actions of , by automorphisms of the torus any measurable conjugacy has to be affine, hence measurable conjugacy implies algebraic conjugacy;
similarly any measurable factor is algebraic, and algebraic and affine centralizers provide invariants of measurable conjugacy.
Using the algebraic machinery of dual modules and information about class numbers of algebraic number fields we construct
various examples of -actions by Bernoulli automorphisms whose measurable orbit structure is rigid, including actions which are weakly isomorphic
but not isomorphic. We show that the structure of the centralizer for these actions may or may not serve as a distinguishing
measure-theoretic invariant.
Received: March 12, 2002 相似文献
10.
Consider a non-connected algebraic group G = G ⋉ Γ with semisimple identity component G and a subgroup of its diagram automorphisms Γ. The identity component G acts
on a fixed exterior component Gτ, id ≠ τ ∈ Γ by conjugation. In this paper we will describe the conjugacy classes and the
invariant theory of this action. Let T be a τ -stable maximal torus of G and its Weyl group W. Then the quotient space Gτ//G
is isomorphic to (T/(1 − τ )(T))/Wτ. Furthermore, exploiting the Jordan decomposition, the reduced fibres of this quotient map are naturally associated bundles
over semisimple G-orbits. Similar to Steinberg's connected and simply connected case [22] and under additional assumptions
on the fundamental group of G, a global section to this quotient map exists. The material presented here is a synopsis of
the Ph.D thesis of the author, cf. [15]. 相似文献
11.
Summary We study closures of conjugacy classes in the Lie algebras of the orthogonal and symplectic groups and determine which ones
are normal varieties. Furthermore we give a complete classification of the minimal singularities which arise in this context,
i.e. the singularities which occur in the open classes in the boundary of a given conjugacy class. In contrast to the results
for the general linear group ([KP1], [KP2]) there are classes with non normal closure; they are branched in a class of codimension
two and give rise to normal minimal singularities. The methods used are (classical) invariant theory and algebraic geometry.
Supported in part by the SFB Theoretische Mathematik, University of Bonn, and by the University of Hamburg 相似文献
12.
Simon M. Goodwin 《Transformation Groups》2006,11(1):51-76
Let G be a simple algebraic group over the algebraically closed field k of characteristic p ≥ 0. Assume p is zero or good
for G. Let B be a Borel subgroup of G; we write U for the unipotent radical of B and u for the Lie algebra of U. Using relative
Springer isomorphisms} we analyze the adjoint orbits of U in u. In particular, we show that an adjoint orbit of U in u contains
a unique so-called minimal representative. In case p > 0, assume G is defined and split over the finite field of p elements
Fp. Let q be a power of p and let G(q) be the finite group of Fq-rational points of G. Let F be the Frobenius morphism such that G(q) = GF. Assume B is F-stable, so that U is also F-stable and U(q) is a Sylow p-subgroup of G(q). We show that the conjugacy classes
of U(q) are in correspondence with the F-stable adjoint orbits of U in u. This allows us to deduce results about the conjugacy
classes of U(q). 相似文献
13.
Walter Ferrer Santos 《代数通讯》2013,41(12):3241-3248
In this paper we prove that if an affine algebraic group (in characteristic zero) has all its conjugacy classes closed, then it is nilpotent. A classical result (called sometimes the Kostant-Rosenlicht Theorem) guarantees that if an affine algebraic group G is unipotent, then all its orbits on affine varieties are closed. We prove the converse of that theorem in arbitrary characteristics. 相似文献
14.
15.
本文首先给出Coxter群中二阶元的判定方法,应用到E6型有限wey1群及A21^(1)型仿射Wey1群,给出了其二阶元的共轭标准形与共轭类数. 相似文献
16.
Let G be a finite group. The question of how certain arithmetical conditions on the lengths of the conjugacy classes of G influence the group structure has been studied by several authors. In this paper we study restrictions on the structure of a finite group in which the lengths of conjugacy classes are not divisible by p 2 for some prime p. We generalise and provide simplified proofs for some earlier results. 相似文献
17.
Philippe Bonnet 《Transformation Groups》2007,12(4):619-630
Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism
Φ, we denote by k(X)Φ its field of invariants, i.e., the set of rational functions f on X such that f o Φ = f. Let n(Φ) be the transcendence degree
of k(X)Φ over k. In this paper we study the class of automorphisms Φ of X for which n(Φ) = dim X - 1. More precisely, we show that
under some conditions on X, every such automorphism is of the form Φ = ϕg, where ϕ is an algebraic action of a linear algebraic group G of dimension 1 on X, and where g belongs to G. As an application,
we determine the conjugacy classes of automorphisms of the plane for which n(Φ) = 1. 相似文献
18.
Hanna Sandler 《Geometriae Dedicata》1998,69(3):317-327
In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ). 相似文献
19.
Piotr ?niady 《Discrete Mathematics》2006,306(7):624-665
The convolution of indicators of two conjugacy classes on the symmetric group Sq is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys-Murphy element involves many conjugacy classes with complicated coefficients. In this article, we consider a combinatorial setup which allows us to manipulate such products easily: to each conjugacy class we associate a two-dimensional surface and the asymptotic properties of the conjugacy class depend only on the genus of the resulting surface. This construction closely resembles the genus expansion from the random matrix theory. As the main application we study irreducible representations of symmetric groups Sq for large q. We find the asymptotic behavior of characters when the corresponding Young diagram rescaled by a factor q-1/2 converge to a prescribed shape. The character formula (known as the Kerov polynomial) can be viewed as a power series, the terms of which correspond to two-dimensional surfaces with prescribed genus and we compute explicitly the first two terms, thus we prove a conjecture of Biane. 相似文献
20.
Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations f(T + K), where K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of T + K, such that f is non constant on each of the components of its domain. 相似文献