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Universal Filtration of Schur Complexes
Proceedings of the American Mathematical Society
Vol. 119, No. 2 (Oct., 1993), pp. 351-355
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2159914
Page Count: 5
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The Schur complex Lλ/μφ has proved useful in studying resolutions of determinantal ideals, both in characteristic zero and in a characteristic-free setting. We show here that in every characteristic, Lλ/μφ is isomorphic, up to a filtration, to a sum of Schur complexes ∑ν γ(λ/μ; ν)Lνφ, where γ(λ/μ; ν) is the usual Littlewood-Richardson coefficient. This generalizes a well-known direct sum decomposition of Lλ/μφ in characteristic zero.
Proceedings of the American Mathematical Society © 1993 American Mathematical Society