Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions

By Ghislain Fourier, P. Littelmann. 2005

201 citations recorded by the source corpus.

We study finite-dimensional representations of current algebras, loop algebras and their quantized versions. For the current algebra of a simple Lie algebra of type ADE, we show that Kirillov?Reshetikhin modules and Weyl modules are in fact all Demazure modules. As a consequence one obtains an elementary proof of the dimension formula for Weyl modules for the current and the loop algebra. Further, we show that the crystals of the Weyl and the Demazure module are the same up to some additional label zero arrows for the Weyl module.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/74b844a76f6a7337347eac88709a3f1ef75b1ebe

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Citations in the corpus

Weyl modules and $$q$$q-Whittaker functions (2012, background): “2 It is important to emphasize that the definition of Demazure modules used in this paper (as fibers of Weyl modules) is not obviously equivalent to the standard definition used in [18]; however, the equivalence of the two definitions is proved in [4] in type A, and in [12] in general.”
On Minimal Affinizations of Representations of Quantum Groups (2006, background): “For example the minimal affinizations of simple Uq (g)-modules of highest weight a multiple of a fundamental weight are the Kirillov-Reshetikhin modules which have been intensively studied in recent years (for example see [KOS, KNH, Kl, HKOTY, KN, Cha2, Nak4, Nak5, H4, CM3, FL ] and references ther”
Kirillov–Reshetikhin crystals for nonexceptional types (2008, background): “ﬁnite tensor product of perfect crystals. This is known as the path realization. Many of the crystals coming from KR modules, KR crystals for short, are (conjectured to be) perfect [8, 9, 18, 31]. By [6, 25] perfect KR crystals are isomorphic as classical crystals to certain Demazure subcrystals of ”
Demazure Modules, Fusion Products and Q-Systems (2013, methodology): “These are generalizations of results which were previously known only for the level one Demazure modules (see [18,33]).”
Weyl modules for the twisted loop algebras (2007, background): “Part (iii) was proved in [6] in the case of sl2, for sln it was proved in [4] and for the general simply laced case in [10].”