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Bijective proofs of shifted tableau and alternating sign matrix identities

Authors:	A M Hamel R C King

Institution:	(1) Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada;(2) School of Mathematics, University of Southampton, Southampton, SO17 1BJ, England

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 ${\prod_{1\leq i < j \leq n} (x_i + y_j)}$ . 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 ${\prod_{1\leq i < j \leq n}(x_i+t^2x_i^{-1}+y_j+t^2y_j^{-1})}$ . 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.

Keywords:	Alternating sign matrices Shifted tableaux Schur P-functions
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