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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On the Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras
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by Shrawan Kumar PDF
J. Amer. Math. Soc. 21 (2008), 797-808 Request permission

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
  • 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