Bijective Proofs of Shifted Tableau and Alternating Sign Matrix Identities
Combinatorics
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0507479,
title = {Bijective Proofs of Shifted Tableau and Alternating Sign Matrix Identities},
author = {A. M. Hamel and R. C. King},
journal= {arXiv preprint arXiv:math/0507479},
year = {2007}
}
Comments
v2: minor revisions