A characterization of Dynkin elements

نویسنده

  • PAUL E. GUNNELLS
چکیده

We give a characterization of the Dynkin elements of a simple Lie algebra. Namely, we prove that one-half of a Dynkin element is the unique point of minimal length in its N -region. In type An this translates into a statement about the regions determined by the canonical left Kazhdan-Lusztig cells.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Minuscule Heaps over Dynkin Diagrams of Type Ã

A minuscule heap is a partially ordered set, together with a labeling of its elements by the nodes of a Dynkin diagram, satisfying certain conditions derived by J. Stembridge. This paper classifies the minuscule heaps over the Dynkin diagram of type Ã.

متن کامل

A Characterization of the Suzuki Groups by Order and the Largest Elements Order

One of the important problems in group theory is characterization of a group by a given property, that is, to prove there exist only one group with a given property. Let  be a finite group. We denote by  the largest order of elements of . In this paper, we prove that some Suzuki groups are characterizable by order and the largest order of elements. In fact, we prove that if  is a group with  an...

متن کامل

On Divisible Weighted Dynkin Diagrams and Reachable Elements

Let G be a connected simple algebraic group with Lie algebra g and e ∈ g a nilpotent element. By the Morozov-Jacobson theorem, there is an sl2-triple containing e, say {e, h, f}. The semisimple element h ∈ g is called a characteristic of e. Let D(e) be the weighted Dynkin diagram of (the G-orbit of) e. As is well known, the numbers occurring in this diagram belong to the set {0, 1, 2} (see Sect...

متن کامل

Root shadow spaces

We give a characterization of the root shadow spaces of buildings whose types correspond to Dynkin diagrams. The results generalize earlier geometric point-line characterizations of certain spherical buildings as well as Timmesfeld’s characterization of abstract root subgroups.

متن کامل

Twining Character Formula of Kac-wakimoto Type for Affine Lie Algebras

We prove a formula of Kac-Wakimoto type for the twining characters of irreducible highest weight modules of symmetric, noncritical, integrally dominant highest weights over affine Lie algebras. This formula describes the twining character in terms of the subgroup of the integral Weyl group consisting of elements which commute with the Dynkin diagram automorphism. The main tools in our proof are...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003