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Monomial Crystals and Partition Crystals

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 21 Apr 2010Embargo end date: 01 Jan 2009 United States Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659, Copyright policy )
Authors: Tingley, Peter William;

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

arXiv: http://arxiv.org/abs/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

Country
United States
Related Organizations
Keywords

crystal basis, Mathematics - Quantum Algebra, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), partition, affine Kac-Moody algebra, Mathematics

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    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).
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    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.
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    influence
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
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!
2
Average
Average
Average
Green
gold