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Bijective Proofs of Shifted Tableau and Alternating Sign Matrix Identities

A. M. Hamel·R. C. King
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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 a product of sums of x and y terms. 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 another x and y product. All results are also interpreted in terms of alternating sign matrix identities, including a result regarding subsets of ASMs specified by conditions on certain restricted column sums.

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A. M. Hamel, R. C. King. 2006-03-02. Bijective Proofs of Shifted Tableau and Alternating Sign Matrix Identities. https://arxiv.org/abs/math/0507479

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