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Monomial Crystals and Partition Crystals

Monomial crystals and partition crystals
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 21 Apr 2010Embargo end date: 01 Jan 2009Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659, Copyright policy )Funded by:NSF | PostDoctoral Research Fel...
Authors: Tingley, Peter William;

doi: 10.3842/sigma.2010.035 , 10.48550/arxiv.0909.2242

arXiv: 0909.2242

handle: 1721.1/89652

Monomial Crystals and Partition Crystals

Abstract

Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal for affine sl(n), where the vertices are indexed by certain partitions. He showed that special cases of this construction agree with the Misra-Miwa realization and with Berg's ladder crystal. Here we show that another special case is naturally isomorphic to a realization using Nakajima's monomial crystal.

4 figures; v2: minor edits for clarity; v3: published version

Related Organizations
Keywords

monomial crystal, Quantum groups (quantized enveloping algebras) and related deformations, partition, crystal basis, Combinatorial aspects of representation theory, Mathematics - Quantum Algebra, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), fundamental crystal, Mathematics, affine Kac-Moody algebra

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average
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