Crystal graphs of irreducible U_v(sl_e)-modules of level two and Uglov bipartitions

2006/07/11 by Nicolas Jacon, Jacon, Nicolas
Chemistry · Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #math.QA #math.RT #msc:17B37 #msc:20C08

paper · pdf · doi:10.48550/arxiv.math/0607251

arxiv created 2006/07/11 · arxiv updated 2009/12/01

Abstract

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 U_v(\mathfraksl_e)-modules of level two, naturally appear in the context of the modular representation theory of Hecke algebras of type B_n.

Related

• Dipper-James-Murphy's conjecture for Hecke algebras of type B
• Parameterizing Hecke algebra modules: Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and crystal graphs
• Uglov bipartitions and extended Young diagrams
• Crystal structures arising from representations of GL(m|n)
• B₂-crystals: axioms, structure, models