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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
Published electronically: March 14, 2008
MathSciNet review: 2393427
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Abstract: We prove a part of the Cachazo-Douglas-Seiberg-Witten conjecture uniformly for any simple Lie algebra $ \mathfrak{g}$. The main ingredients in the proof are: Garland's result on the Lie algebra cohomology of $ \hat{\mathfrak{u}} := \mathfrak{g}\otimes t\mathbb{C}[t]$; Kostant's result on the `diagonal' cohomolgy of $ \hat{\mathfrak{u}}$ and its connection with abelian ideals in a Borel subalgebra of $ \mathfrak{g}$; 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

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.