Abstract
A determinantal expansion due to Okada is used to derive both a deformation of Weyl's denominator formula for the Lie algebra sp(2n) of the symplectic group and a further generalisation involving a product of the deformed denominator with a deformation of flagged characters of sp(2n). In each case the relevant expansion is expressed in terms of certain shifted sp(2n)-standard tableaux. It is then re-expressed, first in terms of monotone patterns and then in terms of alternating sign matrices.
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Hamel, A., King, R. Symplectic Shifted Tableaux and Deformations of Weyl's Denominator Formula for sp(2n). Journal of Algebraic Combinatorics 16, 269–300 (2002). https://doi.org/10.1023/A:1021804505786
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DOI: https://doi.org/10.1023/A:1021804505786