Geodesic
Bijective proofs of shifted tableau and alternating sign matrix identities
Journal of Algebraic Combinatorics, Tome 25 (2007) no. 4, pp. 417-458.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 Õ $_{1 \sterling i j \sterling n} ( x _{ i} + y _{ j})$ prod_$1\leq $i j $\leq n$ (x_i + y_j). 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 $s$p($2 n$)-standard tableaux which are bijectively related to the product of a $t$-deformed $s$p($2 n$) character and Õ $_{1 \sterling i j \sterling n}( x _{ i}+ t ^{2} x _{ i} ^{ -1}+ y _{ j}+ t ^{2} y _{ j} ^{ -1})$ prod_$1\leq $i j $\leq n$(x_i+t^2x_i^-1+y_j+t^2y_j^-1). All results are also interpreted in terms of alternating sign matrix (ASM) identities, including a result regarding subsets of ASMs specified by conditions on certain restricted column sums.
Keywords: keywords alternating sign matrices, shifted tableaux, Schur P-functions 
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     title = {Bijective proofs of shifted tableau and alternating sign matrix identities},
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Hamel, A.M.; King, R.C. Bijective proofs of shifted tableau and alternating sign matrix identities. Journal of Algebraic Combinatorics, Tome 25 (2007) no. 4, pp. 417-458. http://geodesic.mathdoc.fr/item/JAC_2007__25_4_a1/