Symplectic shifted tableaux and deformations of Weyl's denominator formula for sp(2n)
Symplectic shifted tableaux and deformations of Weyl's denominator formula for sp(2n)
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.
alternating sign matrices, symplectic shifted tableau, monotone triangle, Weyl's denominator formula
269-300
Hamel, A.M.
f6d895ef-50b1-4c1c-994f-a6ea3544a715
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
2002
Hamel, A.M.
f6d895ef-50b1-4c1c-994f-a6ea3544a715
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Hamel, A.M. and King, R.C.
(2002)
Symplectic shifted tableaux and deformations of Weyl's denominator formula for sp(2n).
Journal of Algebraic Combinatorics, 16 (3), .
(doi:10.1023/A:1021804505786).
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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Published date: 2002
Keywords:
alternating sign matrices, symplectic shifted tableau, monotone triangle, Weyl's denominator formula
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Local EPrints ID: 29529
URI: http://eprints.soton.ac.uk/id/eprint/29529
ISSN: 0925-9899
PURE UUID: 10076e98-c79f-4652-85b1-46d7484ac909
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Date deposited: 11 May 2006
Last modified: 15 Mar 2024 07:32
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Author:
A.M. Hamel
Author:
R.C. King
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