Kirillov-reshetikhin crystals for nonexceptional types

Fourier, G., Okado, M. and Schilling, A. (2009) Kirillov-reshetikhin crystals for nonexceptional types. Advances in Mathematics, 222(3), pp. 1080-1116. (doi: 10.1016/j.aim.2009.05.020)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fourier, Dr Ghislain
• Authors: Fourier, G., Okado, M., and Schilling, A.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Advances in Mathematics
• ISSN: 0001-8708
• ISSN (Online): 1090-2082