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ISSN 1079-6762

A one-box-shift morphism between Specht modules

Author(s): Matthias Künzer
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 90-94.
MSC (2000): Primary 20C30
Posted: October 5, 2000
MathSciNet review: 1783092
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Abstract:

We give a formula for a morphism between Specht modules over $(\mbox{\rm\bf Z}/m){\CMcal S}_n$ , 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, being the box shift length. Our morphism can be reinterpreted integrally as an extension of order of the corresponding Specht lattices.

References:

1.: R. W. Carter and G. Lusztig, On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 139-242. MR 50:7364
2.: 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. MR 81h:20048
3.: G. D. James, The representation theory of the symmetric groups, SLN 682, 1978. MR 80g:20019
4.: M. Künzer, Ties for the $\mbox{\rm\bf Z}\CMcal{S}_n$ , thesis, http://www.mathematik.uni-bielefeld.de/ $\scriptstyle\sim$ kuenzer, Bielefeld, 1999.

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