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Modular irreducible representations of the symmetric group as linear codes

Title data

Kerber, Adalbert ; Kohnert, Axel:
Modular irreducible representations of the symmetric group as linear codes.
In: European Journal of Combinatorics. Vol. 25 (November 2004) Issue 8 . - pp. 1285-1299.
ISSN 0195-6698
DOI: https://doi.org/10.1016/j.ejc.2003.10.009

Abstract in another language

We describe a particularly easy way of evaluating the modular irreducible matrix representations of the symmetric group. It shows that Specht’s approach to the ordinary irreducible representations, along Specht polynomials, can be unified with Clausen’s approach to the modular irreducible representations using symmetrized standard bideterminants. The unified method, using symmetrized Specht polynomials, is very easy to explain, and it follows directly from Clausen’s theorem by replacing the indeterminate xij of the letter place algebra by xji.

Our approach is implemented in SYMMETRICA. It was used in order to obtain computational results on code theoretic properties of the p-modular irreducible representation [λ]p corresponding to a p-regular partition λ via embedding it into representation spaces obtained from ordinary irreducible representations. The first embedding is into the permutation representation induced from the column group of a standard Young tableau of shape λ. The second embedding is the embedding of [λ]p into the space of , the p-modular representation obtained from the ordinary irreducible representation [λ] by reducing the coefficients modulo p.

We include a few tables with dimensions and minimum distances of these codes; others can be found via our home page.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Jun 2015 05:16
Last Modified: 19 Jun 2015 05:16
URI: https://eref.uni-bayreuth.de/id/eprint/15290