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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Root components for tensor product of affine Kac-Moody Lie algebra modules
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by Samuel Jeralds and Shrawan Kumar
Represent. Theory 26 (2022), 825-858
Published electronically: July 26, 2022


Let $\mathfrak {g}$ be an affine Kac-Moody Lie algebra and let $\lambda , \mu$ be two dominant integral weights for $\mathfrak {g}$. We prove that under some mild restriction, for any positive root $\beta$, $V(\lambda )\otimes V(\mu )$ contains $V(\lambda +\mu -\beta )$ as a component, where $V(\lambda )$ denotes the integrable highest weight (irreducible) $\mathfrak {g}$-module with highest weight $\lambda$. This extends the corresponding result by Kumar from the case of finite dimensional semisimple Lie algebras to the affine Kac-Moody Lie algebras. One crucial ingredient in the proof is the action of Virasoro algebra via the Goddard-Kent-Olive construction on the tensor product $V(\lambda )\otimes V(\mu )$. Then, we prove the corresponding geometric results including the higher cohomology vanishing on the $\mathcal {G}$-Schubert varieties in the product partial flag variety $\mathcal {G}/\mathcal {P}\times \mathcal {G}/\mathcal {P}$ with coefficients in certain sheaves coming from the ideal sheaves of $\mathcal {G}$-sub-Schubert varieties. This allows us to prove the surjectivity of the Gaussian map.
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Bibliographic Information
  • Samuel Jeralds
  • Affiliation: School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia
  • ORCID: 0000-0003-3109-7733
  • Email:
  • Shrawan Kumar
  • Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
  • MR Author ID: 219351
  • Email:
  • Received by editor(s): July 14, 2021
  • Received by editor(s) in revised form: April 21, 2022
  • Published electronically: July 26, 2022
  • Additional Notes: The second author was partially supported by the NSF grant number DMS-1802328.
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 825-858
  • MSC (2020): Primary 14M15, 14M17, 20G44, 22E47
  • DOI:
  • MathSciNet review: 4457456