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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Universal filtration of Schur complexes


Author: Giandomenico Boffi
Journal: Proc. Amer. Math. Soc. 119 (1993), 351-355
MSC: Primary 13D25; Secondary 20G05
MathSciNet review: 1169021
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Abstract: The Schur complex $ {{\mathbf{L}}_{\lambda /\mu }}\phi $ 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, $ {{\mathbf{L}}_{\lambda /\mu }}\phi $ is isomorphic, up to a filtration, to a sum of Schur complexes $ \sum\nolimits_\nu {\gamma (\lambda /\mu ;\nu ){{\mathbf{L}}_\nu }\phi } $, where $ \gamma (\lambda /\mu ;\nu )$ is the usual Littlewood-Richardson coefficient. This generalizes a well-known direct sum decomposition of $ {{\mathbf{L}}_{\lambda /\mu }}\phi $ in characteristic zero.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1169021-4
PII: S 0002-9939(1993)1169021-4
Article copyright: © Copyright 1993 American Mathematical Society