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Kus, Deniz (2013). Realization of affine type A Kirillov-Reshetikhin crystals via polytopes. J. Comb. Theory Ser. A, 120 (8). S. 2093 - 2118. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-0899

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Abstract

On the polytope defined by Feigin, Fourier and Littelmann, associated to any highest weight corresponding to a rectangular partition, we define a crystal structure of type A(n). We show that this crystal is isomorphic to the one obtained from Kashiwara's crystal bases theory. Further we define on this polytope a bijective map and show that this map satisfies the properties of a weak promotion operator. This implies in particular that we provide an explicit realization of Kirillov-Reshetikhin crystals for the affine type A(n)((1)) via polytopes. (c) 2013 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kus, Deniz UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-473223
DOI:	10.1016/j.jcta.2013.08.009
Journal or Publication Title:	J. Comb. Theory Ser. A
Volume:	120
Number:	8
Page Range:	S. 2093 - 2118
Date:	2013
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1096-0899
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Q-ANALOG; MODULES; BASES; REPRESENTATIONS; PATHS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47322