A one-box-shift morphism between Specht modules
Author:
Matthias Künzer
Journal:
Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 90-94
MSC (2000):
Primary 20C30
DOI:
https://doi.org/10.1090/S1079-6762-00-00085-8
Published electronically:
October 5, 2000
MathSciNet review:
1783092
Full-text PDF Free Access
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Abstract: We give a formula for a morphism between Specht modules over $(\mathbf {Z}/m)\mathcal {S}_n$, where $n\geq 1$, and where the partition indexing the target Specht module arises from that indexing the source Specht module by a downwards shift of one box, $m$ being the box shift length. Our morphism can be reinterpreted integrally as an extension of order $m$ of the corresponding Specht lattices.
- Roger W. Carter and George Lusztig, On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 193–242. MR 354887, DOI https://doi.org/10.1007/BF01214125
- R. W. Carter and M. T. J. Payne, On homomorphisms between Weyl modules and Specht modules, Math. Proc. Cambridge Philos. Soc. 87 (1980), no. 3, 419–425. MR 556922, DOI https://doi.org/10.1017/S0305004100056851
- G. D. James, The representation theory of the symmetric groups, Lecture Notes in Mathematics, vol. 682, Springer, Berlin, 1978. MR 513828
K99 M. Künzer, Ties for the $\mathbb {Z}\mathcal {S}_n$, thesis, http://www.mathematik.uni-bielefeld.de/~kuenzer, Bielefeld, 1999.
CL74 R. W. Carter and G. Lusztig, On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 139–242.
CP80 R. W. Carter and M. T. J. Payne, On homomorphisms between Weyl modules and Specht modules, Math. Proc. Camb. Phil. Soc. 87 (1980), 419–425.
J78 G. D. James, The representation theory of the symmetric groups, SLN 682, 1978.
K99 M. Künzer, Ties for the $\mathbb {Z}\mathcal {S}_n$, thesis, http://www.mathematik.uni-bielefeld.de/~kuenzer, Bielefeld, 1999.
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Additional Information
Matthias Künzer
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld
Email:
kuenzer@mathematik.uni-bielefeld.de
Keywords:
Symmetric group,
Specht module
Received by editor(s):
July 14, 2000
Published electronically:
October 5, 2000
Communicated by:
David J. Benson
Article copyright:
© Copyright 2000
American Mathematical Society
