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On the Littlewood-Richardson rule for almost skew-shapes

Authors: Giandomenico Boffi and David A. Buchsbaum
Journal: Proc. Amer. Math. Soc. 136 (2008), 1155-1161
MSC (2000): Primary 05E10, 20G05; Secondary 13D25
Published electronically: December 28, 2007
MathSciNet review: 2367089
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe combinatorially the coefficients occurring in the irreducible decomposition of the Weyl module associated with an almost skew-shape belonging to the family $ J$.

The proof uses the fundamental exact sequence for almost skew-shapes to initiate an inductive procedure which ultimately reduces to the classical Littlewood-Richardson rule for skew partitions.

References [Enhancements On Off] (What's this?)

  • 1. K. Akin and D. A. Buchsbaum, Characteristic-free representation theory of the general linear group, 2. Homological considerations, Adv. Math. 72 (1988), 171-210. MR 972760 (90e:20037)
  • 2. G. Boffi and D. A. Buchsbaum, Threading Homology Through Algebra: Selected Patterns, Oxford University Press (Clarendon), Oxford 2006. MR 2247272 (2007g:13018)
  • 3. I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press (Clarendon), Oxford 1979. MR 553598 (84g:05003)

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Additional Information

Giandomenico Boffi
Affiliation: Dipartimento di Scienze, Università “G. d’Annunzio”, Viale Pindaro 42, 65127 Pescara, Italy

David A. Buchsbaum
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254

Keywords: Almost skew-shape, Weyl module, Littlewood-Richardson rule
Received by editor(s): September 4, 2006
Published electronically: December 28, 2007
Additional Notes: The first author was partially supported by MIUR and is a member of GNSAGA - INdAM
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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