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Bijective proofs of shifted tableau and alternating sign matrix identities

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
0925-9899
417-458
Hamel, A.M
165799e3-3e71-48de-a113-6bbbd0d7a5ec
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
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), 417-458. (doi:10.1007/s10801-006-0044-1).

Record type: Article

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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More information

Published date: June 2007
Keywords: alternating sign matrices, shifted tableaux, schur p-functions

Identifiers

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: 08 Jan 2022 01:09

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Contributors

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

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