Symplectic Shifted Tableaux and Deformations of Weyl's Denominator Formula for sp(2n) |
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| Authors: | A.M. Hamel R.C. King |
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| Affiliation: | (1) Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada;(2) Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, UK |
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| 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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| Keywords: | alternating sign matrices symplectic shifted tableau monotone triangle Weyl's denominator formula |
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