Séminaire Lotharingien de Combinatoire, 78B.47 (2017), 12 pp.
Emily Gunawan and Travis Scrimshaw
Realization of Kirillov-Reshetikhin Crystals B1,s for
sl^n Using Nakajima Monomials
We give a realization of the Kirillov-Reshetikhin crystal
sl^n using Nakajima monomials using the
crystal structure given by Kashiwara. We describe the tensor product
B1,si in terms of a shift of indices,
allowing us to recover the Kyoto path model. We give a description of
the limit of the coherent family of crystals
using Nakajima monomials, which allows us
to recover the path model for
B(\infty). Additionally, we realize
the KR crystals
using Nakajima monomials.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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