Crystal graphs of irreducible $U_v(\hat{sl}_e)$-modules of level two and Uglov bipartitions

Details Crystal graphs of irreducible $U_v(\hat{sl}_e)$-modules of level two and Uglov bipartitions Crystal graphs of irreducible $U_v(\hat{sl}_e)$-modules of level two and Uglov bipartitions

2006-07-11

arxiv.org/abs/math/0607251v1

Mathematics

Representation Theory

Scientific paper

We give a simple description of the natural bijection between the set of FLOTW bipartitions and the set of Uglov bipartitions (which generalizes the set of Kleshchev bipartitions). These bipartitions, which label the crystal graphs of irreducible $\mathcal{U}\_v({\hat{\mathfrak{sl}}\_e})$-modules of level two, naturally appear in the context of the modular representation theory of Hecke algebras of type $B\_n$.

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