Symplectic shifted tableaux and deformations of Weyl's denominator formula for \(\text{sp}(2n)\) (Q1863001)

The authors consider the most natural deformation of Weyl's denominator formula in the case of the Lie algebra \(\text{sp}(2n)\) and derive the analogon to Tokuyama's result (concerning the case \(\text{sl}(n)\)) [J. Math. Soc. Japan 40, No. 4, 671--685 (1988; Zbl 0639.20022)]. The derivation involves (an extension of) a determinantal expansion due to \textit{S. Okada} [J. Algebr. Comb. 2, No. 2, 155--176 (1993; Zbl 0781.15008)]. This expansion is expressed in terms of certain shifted \(\text{sp}(2n)\)-standard tableaux in the first place, and then re-expressed in terms of monotonic patterns and in terms of alternating sign matrices.