Kirillov--Reshetikhin crystals for nonexceptional types

Details Kirillov--Reshetikhin crystals for nonexceptional types Kirillov--Reshetikhin crystals for nonexceptional types

2008-10-28

arxiv.org/abs/0810.5067v2

Adv.Math.222:1080-1116,2009

Mathematics

Representation Theory

35 pages; typos fixed; to appear in Advances in Mathematics

Scientific paper

10.1016/j.aim.2009.05.020

We provide combinatorial models for all Kirillov--Reshetikhin crystals of nonexceptional type, which were recently shown to exist. For types D_n^(1), B_n^(1), A_{2n-1}^(2) we rely on a previous construction using the Dynkin diagram automorphism which interchanges nodes 0 and 1. For type C_n^(1) we use a Dynkin diagram folding and for types A_{2n}^(2), D_{n+1}^(2) a similarity construction. We also show that for types C_n^(1) and D_{n+1}^(2) the analog of the Dynkin diagram automorphism exists on the level of crystals.

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