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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
Full-text PDF Free Access
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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  . 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.
- 1.
Kaan
Akin and David
A. Buchsbaum, Characteristic-free representation theory of the
general linear group. II. Homological considerations, Adv. in Math.
72 (1988), no. 2, 171–210. MR 972760
(90e:20037), http://dx.doi.org/10.1016/0001-8708(88)90027-8
- 2.
Giandomenico
Boffi and David
A. Buchsbaum, Threading homology through algebra: selected
patterns, Oxford Mathematical Monographs, The Clarendon Press, Oxford
University Press, Oxford, 2006. Oxford Science Publications. MR 2247272
(2007g:13018)
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I.
G. Macdonald, Symmetric functions and Hall polynomials, The
Clarendon Press, Oxford University Press, New York, 1979. Oxford
Mathematical Monographs. MR 553598
(84g:05003)
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- 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
Email:
gboffi@unich.it
David A. Buchsbaum
Affiliation:
Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254
Email:
buchsbau@brandeis.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-07-09339-2
PII:
S 0002-9939(07)09339-2
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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