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
Abstract.
We give a realization of the Kirillov-Reshetikhin crystal
B1,s
for
sl^n using Nakajima monomials using the
crystal structure given by Kashiwara. We describe the tensor product
\bigotimesi=1N
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
{B1,s}s=1\infty
using Nakajima monomials, which allows us
to recover the path model for
B(\infty). Additionally, we realize
the KR crystals
Br,1 for
sl^n
using Nakajima monomials.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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