A Note on De Concini and Procesi’s Curious Identity

نویسنده

  • GRAHAM DENHAM
چکیده

We give a short, case-free and combinatorial proof of de Concini and Procesi’s formula from [1] for the volume of the simplicial cone spanned by the simple roots of any finite root system. The argument presented here also extends their formula to include the non-crystallographic root systems.

برای دانلود رایگان 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

A Curious Identity and the Volume of the Root Spherical Simplex

In this note we shall consider a finite root system R spanning an euclidean space E of dimension l (for all the facts about root systems which we are going to use in this note we refer to [1]). l is called the rank of R. We shall choose once and for all a set of positive roots R+ and in R+ the set of simple roots ∆ = {α1, . . . , αl}. We shall also denote by W the Weyl group of R i.e. the finit...

متن کامل

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...

متن کامل

A curious binomial identity

In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients.

متن کامل

The homology of real subspace arrangements

Associated to any subspace arrangement is a ‘De Concini–Procesi model’, a certain smooth compactification of its complement, which in the case of the braid arrangement produces the Deligne–Mumford compactification of the moduli space of genus 0 curves with marked points. In the present work, we calculate the integral homology of real De Concini–Procesi models, extending earlier work of Etingof,...

متن کامل

Abelianizing the Real Permutation Action via Blowups

Our object of study is an abelianization of the Sn permutation action on R n that is provided by a particular De Concini-Procesi wonderful model for the braid arrangement. Our motivation comes from an analogous construction for finite group actions on complex manifolds, due to Batyrev [B1, B2], and subsequent study of Borisov & Gunnells [BG], where the connection of such abelianizations with De...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007