Bijective proofs of shifted tableau and alternating sign matrix identities
Bijective proofs of shifted tableau and alternating sign matrix identities
We give a bijective proof of an identity relating primed shifted
gl(n)-standard tableaux to the product of a gl(n) character in the form of a Schur function and ?l?i<j?n(xi + yj). This result generalises a number of well--known results due to Robbins and Rumsey, Chapman, Tokuyama, Okada and Macdonald. An analogous result is then obtained in the case of
primed shifted sp(2n)-standard tableaux which are bijectively
related to the product of a t-deformed sp(2n) character and
?l?i<j?n(xi + t^2xi^-1 + yj + t^2yj^-1). All results are also interpreted in terms of alternating sign matrix
(ASM) identities, including a result regarding subsets of ASMs
specified by conditions on certain restricted column sums.
alternating sign matrices, shifted tableaux, schur p-functions
417-458
Hamel, A.M
165799e3-3e71-48de-a113-6bbbd0d7a5ec
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
June 2007
Hamel, A.M
165799e3-3e71-48de-a113-6bbbd0d7a5ec
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Hamel, A.M and King, R.C.
(2007)
Bijective proofs of shifted tableau and alternating sign matrix identities.
Journal of Algebraic Combinatorics, 25 (4), .
(doi:10.1007/s10801-006-0044-1).
Abstract
We give a bijective proof of an identity relating primed shifted
gl(n)-standard tableaux to the product of a gl(n) character in the form of a Schur function and ?l?i<j?n(xi + yj). This result generalises a number of well--known results due to Robbins and Rumsey, Chapman, Tokuyama, Okada and Macdonald. An analogous result is then obtained in the case of
primed shifted sp(2n)-standard tableaux which are bijectively
related to the product of a t-deformed sp(2n) character and
?l?i<j?n(xi + t^2xi^-1 + yj + t^2yj^-1). All results are also interpreted in terms of alternating sign matrix
(ASM) identities, including a result regarding subsets of ASMs
specified by conditions on certain restricted column sums.
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Published date: June 2007
Keywords:
alternating sign matrices, shifted tableaux, schur p-functions
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Local EPrints ID: 50559
URI: http://eprints.soton.ac.uk/id/eprint/50559
ISSN: 0925-9899
PURE UUID: 06b4fd8d-2beb-404d-a1c0-3d939f7ac98d
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Date deposited: 03 Mar 2008
Last modified: 15 Mar 2024 10:07
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Author:
A.M Hamel
Author:
R.C. King
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