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

Se jin Oh

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We extend the Andrews-Olsson identity to two-colored partitions. Regarding the sets of proper Young walls of quantum affine algebras gn=A2n(2), A2n-1(2), Bn(1), Dn(1) and Dn+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:. ∏i=1∞(1+ti)κi where κ i = 0, 1 or2, and κi 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(Λ) of the level 1 highest weight modules V(Λ) over Uq(gn).

Original languageEnglish
Pages (from-to)8-31
Number of pages24
JournalEuropean Journal of Combinatorics
StatePublished - Jan 2015

Bibliographical note

Funding Information:
This work was supported by BK21 PLUS SNU Mathematical Sciences Division.


Dive into the research topics of 'The Andrews-Olsson identity and Bessenrodt insertion algorithm on Young walls'. Together they form a unique fingerprint.

Cite this