Demazure module: Difference between revisions

Revision as of 13:45, 28 July 2011

Revision as of 13:48, 28 July 2011

Line 1:

In mathematics, the '''Demazure character formula''' is a generalization of the [[Weyl character formula]] for the characters of finite dimensional representations of [[semisimple Lie algebra]]s, introduced by {{harvs|txt|authorlink=Michel Demazure|last=Demazure|year=1974a|year2=1974b|loc2=theorem 2}}. Demazure's formula gives the character of the submodule of a finite dimensional representation generated by an extremal weight under the action of the unipotent radical of a Borel subalgebra.

Victor Kac pointed out that Demazure's original proof of the character formula washas a serious gap, as incorrect: Proposition 11 of Section 2 of {{harvtxt|Demazure|1974a}} is false. {{harvtxt|Anderson|1985}} later gave a proof of Demazure's character formula using the work on the geometry of [[Schubert varieties]] by {{harvtxt|Ramanan|Ramanathan|1985}}, and {{harvtxt|Joseph|1985}} gave a proof for genericsufficiently large dominant highest weight modules using Lie algebra techniques.

==References==