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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.
Received: February 10, 2010; in final form April 12, 2010; Published online April 21, 2010
Citation:
Peter Tingley, “Monomial Crystals and Partition Crystals”, SIGMA, 6 (2010), 035, 8 pp.
Linking options:
https://www.mathnet.ru/eng/sigma492 https://www.mathnet.ru/eng/sigma/v6/p35
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Abstract page: | 217 | Full-text PDF : | 34 | References: | 27 |
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