Abstract
Many different definitions have been given for semistandard odd and even orthogonal tableaux which enumerate the corresponding irreducible orthogonal characters. Weightpreserving bijections have been provided between some of these sets of tableaux (see [3], [8]). We give bijections between the (semistandard) odd orthogonal Koike-Terada tableaux and the odd orthogonal Sundaram-tableaux and between the even orthogonal Koike-Terada tableaux and the even orthogonal King-Welsh tableaux. As well, we define an even version of orthogonal Sundaram tableaux which enumerate the irreducible characters of O(2n).
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A. Stokke was supported by a grant from the National Sciences and Engineering Research Council of Canada.
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Campbell, P.S., Stokke, A. On the Orthogonal Tableaux of Koike and Terada. Ann. Comb. 17, 443–453 (2013). https://doi.org/10.1007/s00026-013-0191-8
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DOI: https://doi.org/10.1007/s00026-013-0191-8