Bijective proofs of shifted tableau and alternating sign matrix identities
Hamel, A.M and King, R.C. (2007) Bijective proofs of shifted tableau and alternating sign matrix identities. Journal of Algebraic Combinatorics, 25, (4), 417-458. (doi:10.1007/s10801-006-0044-1)
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Official URL: http://dx.doi.org/10.1007/s10801-006-0044-1
Description/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 ∏l≤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
∏l≤i<j≤n(xi + t^2xi^-1 + yj + t^2yj^-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.
| Item Type: | Article |
|---|---|
| ISSN: | 0925-9899 (print) |
| Uncontrolled Keywords: | alternating sign matrices, shifted tableaux, schur p-functions |
| Related URLs: | http://dx.doi.org/10.1007/s108...006-0044-1 |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics |
| ePrint ID: | 50559 |
| Deposited On: | 03 Mar 2008 |
| Last Modified: | 01 Sep 2011 18:32 |
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