On the Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras

Author:
Shrawan Kumar

Journal:
J. Amer. Math. Soc. **21** (2008), 797-808

MSC (2000):
Primary 22E70, 22E67

DOI:
https://doi.org/10.1090/S0894-0347-08-00599-7

Published electronically:
March 14, 2008

MathSciNet review:
2393427

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a part of the Cachazo-Douglas-Seiberg-Witten conjecture uniformly for any simple Lie algebra . The main ingredients in the proof are: Garland's result on the Lie algebra cohomology of ; Kostant's result on the `diagonal' cohomolgy of and its connection with abelian ideals in a Borel subalgebra of ; and a certain deformation of the singular cohomology of the infinite Grassmannian introduced by Belkale-Kumar.

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Additional Information

**Shrawan Kumar**

Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599–3250

Email:
shrawan@email.unc.edu

DOI:
https://doi.org/10.1090/S0894-0347-08-00599-7

Keywords:
Simple Lie algebra,
infinite Grassmannian,
Abelian ideal

Received by editor(s):
March 15, 2006

Published electronically:
March 14, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.