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Minimal affinizations of representations of quantum groups: The nonsimply-laced case

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Abstract

If U q (g) is a finite-dimensional complex simple Lie algebra, an affinization of a finite-dimensional irreducible representationV of U q (g) is a finite-dimensional irreducible representation\(\hat V\) of U q (ĝ) which containsV with multiplicity one, and is such that all other U q (g)-types in\(\hat V\) have highest weights strictly smaller than that ofV. There is a natural partial ordering\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } \) on the set of affinizations, defined by Chari. In this Letter, we describe the minimal affinizations, with respect to\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } \), when g is not simply-laced.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92521, Riverside, CA, USA

    Vyjayanthi Chari

  2. Department of Mathematics, King's College, Strand, WC2R 2LS, London, U.K.

    Andrew Pressley

Authors
  1. Vyjayanthi Chari
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  2. Andrew Pressley
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Both authors were partially supported by the NSF, DMS-9207701.

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Chari, V., Pressley, A. Minimal affinizations of representations of quantum groups: The nonsimply-laced case. Lett Math Phys 35, 99–114 (1995). https://doi.org/10.1007/BF00750760

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