Kleshchev multipartitions and extended Young diagrams

2017/06/23 by Nicolas Jacon, Jacon, Nicolas
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1706.07595

Correction of a gap in the proof of the main Theorem. The Theorem is generalized to all types of Uglov multipartitions. Final version

arxiv created 2018/09/19 · arxiv updated 2018/09/20

Abstract

We give a new simple characterization of the set of Kleshchev multipartitions, and more generally of the set of Uglov multipartitions. These combinatorial objects play an important role in various areas of representation theory of quantum groups, Hecke algebras or finite reductive groups. As a consequence, we obtain a proof of a generalization of a conjecture by Dipper, James and Murphy and a generalization of the LLT algorithm for arbitrary level.

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