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

Kumar, Shrawan

doi:10.1090/S0894-0347-08-00599-7

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.

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