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

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- by Shrawan Kumar
- J. Amer. Math. Soc.
**21**(2008), 797-808 - DOI: https://doi.org/10.1090/S0894-0347-08-00599-7
- Published electronically: March 14, 2008
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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.## References

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## Bibliographic Information

**Shrawan Kumar**- Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599–3250
- MR Author ID: 219351
- Email: shrawan@email.unc.edu
- Received by editor(s): March 15, 2006
- Published electronically: March 14, 2008
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2393427