## Elliptic central characters and blocks of finite dimensional representations of quantum affine algebras

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- by Pavel I. Etingof and Adriano A. Moura
- Represent. Theory
**7**(2003), 346-373 - DOI: https://doi.org/10.1090/S1088-4165-03-00201-2
- Published electronically: August 26, 2003
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## Abstract:

The category of finite dimensional (type 1) representations of a quantum affine algebra $U_q(\widehat {{\mathfrak g}})$ is not semisimple. However, as any abelian category with finite-length objects, it admits a unique decomposition in a direct sum of indecomposable subcategories (blocks). We define the elliptic central character of a finite dimensional (type 1) representation of $U_q(\widehat {{\mathfrak g}})$ and show that the block decomposition of this category is parametrized by these elliptic central characters.## References

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## Bibliographic Information

**Pavel I. Etingof**- Affiliation: Massachussets Institute of Technology, 77 Massachussets Ave., Room 2-176, Cambridge, Massachusetts 02139
- MR Author ID: 289118
- Email: etingof@math.mit.edu
**Adriano A. Moura**- Affiliation: IMECC/UNICAMP, Caixa Postal: 6065, CEP: 13083-970, Campinas SP Brazil
- Email: adrianoam@ime.unicamp.br
- Received by editor(s): April 24, 2002
- Received by editor(s) in revised form: December 10, 2002
- Published electronically: August 26, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Represent. Theory
**7**(2003), 346-373 - MSC (2000): Primary 20G42
- DOI: https://doi.org/10.1090/S1088-4165-03-00201-2
- MathSciNet review: 2017062

Dedicated: For Igor Frenkel, on the occasion of his 50th birthday