2005/07/22 by Angèle M. Hamel, A. M. Hamel, Hamel, A. M. +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.CO #msc:05E10
paper · pdf · doi:10.48550/arxiv.math/0507479
v2: minor revisions
arxiv created 2006/03/02 · arxiv updated 2009/12/01
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.