Weyl modules, Demazure modules and finite crystals for non-simply laced type

Abstract

We show that every Weyl module for a current algebra has a filtration whose successive quotients are isomorphic to Demazure modules, and that the path model for a tensor product of level zero fundamental representations is isomorphic to a disjoint union of Demazure crystals. Moreover, we show that the Demazure modules appearing in these two objects coincide exactly. Though these results have been previously known in the simply laced case, they are new in the non-simply laced case.

54pages, added references, corrected typos and unclear expressions

References in corpus (2)

• Current algebras, highest weight categories and quivers
• Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas

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• Bases for local Weyl modules in type $C$
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