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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)
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
0925-9899
269-300
Hamel, A.M.
f6d895ef-50b1-4c1c-994f-a6ea3544a715
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
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), 269-300. (doi:10.1023/A:1021804505786).

Record type: Article

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: 08 Jan 2022 03:51

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Contributors

Author: A.M. Hamel
Author: R.C. King

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