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PERFECT CRYSTALS FOR THE QUANTUM AFFINE ALGEBRA

Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-747, Korea

This research was supported by KRF Grant # 2007-341-C00001.

This research was supported by National Institute for Mathematical Sciences (2010 Thematic Program, TP1004).

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MYUNGHO KIM

Department of Mathematical Sciences, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-747, Korea

This research was supported by KRF Grant # 2007-341-C00001.

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INHA LEE

Department of Mathematical Sciences, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-747, Korea

This research was supported by KRF Grant # 2007-341-C00001.

This research was supported by BK21 Mathematical Sciences Division.

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KAILASH C. MISRA

Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA

This research was supported by NSA Grant # H98230-08-1-0080.

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https://doi.org/10.1142/9789814324373_0008Cited by:0 (Source: Crossref)

Abstract:

In this paper, we give an explicit isomorphism between the adjoint crystal 𝔹_ℓ given in Ref. 13 and the Kirillov-Reshetikhin crystals B^1,2ℓ presented in Ref. 2 for . Consequently we have a complete proof of perfectness of the crystals 𝔹_ℓ. In the sequel we also present an explicit description of the involution σ given in Ref. 2 for this special case.

Dedication: Dedicated to Professor Tetsuji Miwa on the occasion of his 60th birthday

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PERFECT CRYSTALS FOR THE QUANTUM AFFINE ALGEBRA

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