Bijective proofs of shifted tableau and alternating sign matrix identities
نویسندگان
چکیده
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 ∏ 1≤i<j≤n(xi + yj). 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 ∏ 1≤i<j≤n(xi + t x i + yj + t y j ). All results are also interpreted in terms of alternating sign matrix identities.
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