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SIGMA, 2010, Volume 6, 035, 8 pages (Mi sigma492)  

This article is cited in 1 scientific paper (total in 1 paper)

Monomial Crystals and Partition Crystals

Peter Tingley

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Abstract: Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal $B(\Lambda_0)$ for $\widehat{\mathfrak{sl}}_\ell$, 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.

Keywords: crystal basis; partition; affine Kac–Moody algebra

DOI: https://doi.org/10.3842/SIGMA.2010.035

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Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/035/
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Bibliographic databases:

ArXiv: 0909.2242
MSC: 17B37; 05E10
Received: February 10, 2010; in final form April 12, 2010; Published online April 21, 2010
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Citation: Peter Tingley, “Monomial Crystals and Partition Crystals”, SIGMA, 6 (2010), 035, 8 pp.

Citation in format AMSBIB
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\paper Monomial Crystals and Partition Crystals
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sam S.V., Tingley P., “Combinatorial Realizations of Crystals Via Torus Actions on Quiver Varieties”, J. Algebr. Comb., 39:2 (2014), 271–300  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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