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
DOI:
https://doi.org/10.1090/S0002-9939-07-09339-2
Published electronically:
December 28, 2007
MathSciNet review:
2367089
Full-text PDF Free Access
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 
.
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, https://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
- 3. I. G. Macdonald, Symmetric functions and Hall polynomials, The Clarendon Press, Oxford University Press, New York, 1979. Oxford Mathematical Monographs. MR 553598
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 05E10, 20G05, 13D25
Retrieve articles in all journals with MSC (2000): 05E10, 20G05, 13D25
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:
https://doi.org/10.1090/S0002-9939-07-09339-2
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.