English

Kirillov--Reshetikhin crystals for nonexceptional types

Representation Theory 2010-01-08 v2 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.0810.5067,
  title  = {Kirillov--Reshetikhin crystals for nonexceptional types},
  author = {Ghislain Fourier and Masato Okado and Anne Schilling},
  journal= {arXiv preprint arXiv:0810.5067},
  year   = {2010}
}

Comments

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