Bijective Proofs of Shifted Tableau and Alternating Sign Matrix Identities

Details Bijective Proofs of Shifted Tableau and Alternating Sign Matrix Identities Bijective Proofs of Shifted Tableau and Alternating Sign Matrix Identities

2005-07-22

arxiv.org/abs/math/0507479v2

Mathematics

Combinatorics

v2: minor revisions

Scientific paper

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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