Existence of Kirillov--Reshetikhin crystals for multiplicity free nodes

Abstract

We show that the Kirillov--Reshetikhin crystal $B^{r,s}$ exists when $r$ is a node such that the Kirillov--Reshetikhin module $W^{r,s}$ has a multiplicity free classical decomposition.

arXiv comment12 pages, 1 figure, 1 table

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Cited by in corpus (5)

• On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models
• Simplicity of tensor products of Kirillov--Reshetikhin modules: nonexceptional affine and G types
• Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types
• Kirillov-Reshetikhin crystals $B^{7,s}$ for type $E_7^{(1)}$
• Perfectness of Kirillov-Reshetikhin Crystals $B^{r,s}$ for types $E_6^{(1)}$ and $E_7^{(1)}$ with a minuscule node $r$