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The Andrews-Olsson identity and Bessenrodt insertion algorithm on Young walls

Title
The Andrews-Olsson identity and Bessenrodt insertion algorithm on Young walls
Authors
Oh, Se-jin
Ewha Authors
오세진
SCOPUS Author ID
오세진scopus
Issue Date
2015
Journal Title
EUROPEAN JOURNAL OF COMBINATORICS
ISSN
0195-6698JCR Link

1095-9971JCR Link
Citation
EUROPEAN JOURNAL OF COMBINATORICS vol. 43, pp. 8 - 31
Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Indexed
SCI; SCIE; SCOPUS WOS
Document Type
Article
Abstract
We extend the Andrews-Olsson identity to two-colored partitions. Regarding the sets of proper Young walls of quantum affine algebras g(n) = A(2n)((2)),A(2n-1)((2)),B-n((1)),D-n((1)) and D-n+1((2)) as the sets of two-colored partitions, the extended Andrews-Olsson identity implies that the generating functions of the sets of reduced Young walls have very simple formulae: Pi(infinity)(i=1)(1 + t(i) )(ki) where k(i) = 0, 1 or 2, and k(i) varies periodically. Moreover, we generalize Bessenrodt's algorithms to prove the extended Andrews-Olsson identity in an alternative way. From these algorithms, we can give crystal structures on certain subsets of pair of strict partitions which are isomorphic to the crystal bases B(Lambda) of the level 1 highest weight modules V (Lambda) over U-q(g(n)). (C) 2014 Elsevier Ltd. All rights reserved.
DOI
10.1016/j.ejc.2014.07.001
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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