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Globally Irreducible Weyl Modules for Quantum Groups

  • Skip GaribaldiEmail author
  • Robert M. Guralnick
  • Daniel K. Nakano
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)

Abstract

The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for \(E_{8}\) or its highest weight is minuscule. In this paper, we prove an analogous criteria for irreducibility of Weyl modules over the quantum group \(U_{\zeta }({\mathfrak {g}})\) where \({\mathfrak {g}}\) is a complex simple Lie algebra and \(\zeta \) ranges over roots of unity.

2010 Mathematics Subject Classification

Primary 20G42 

Notes

Acknowledgements

The authors thank Henning Andersen and George Lusztig for their suggestion to extend our prior work [1] to the quantum case.

References

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Skip Garibaldi
    • 1
    Email author
  • Robert M. Guralnick
    • 2
  • Daniel K. Nakano
    • 3
  1. 1.Center for Communications ResearchSan DiegoUSA
  2. 2.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of MathematicsUniversity of GeorgiaAthensUSA

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