Maximal ideals in modular group algebras

of the finitary symmetric and

alternating groups

Authors:
Alexander Baranov and Alexander Kleshchev

Journal:
Trans. Amer. Math. Soc. **351** (1999), 595-617

MSC (1991):
Primary 20C05, 16S34

DOI:
https://doi.org/10.1090/S0002-9947-99-02003-6

MathSciNet review:
1443188

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Abstract: The main result of the paper is a description of the maximal ideals in the modular group algebras of the finitary symmetric and alternating groups (provided the characteristic of the ground field is greater than 2). For the symmetric group there are exactly such ideals and for the alternating group there are of them. The description is obtained in terms of the annihilators of certain systems of the `completely splittable' irreducible modular representations of the finite symmetric and alternating groups. The main tools used in the proofs are the modular branching rules (obtained earlier by the second author) and the `Mullineux conjecture' proved recently by Ford-Kleshchev and Bessenrodt-Olsson. The results obtained are relevant to the theory of PI-algebras. They are used in a later paper by the authors and A. E. Zalesskii on almost simple group algebras and asymptotic properties of modular representations of symmetric groups.

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Additional Information

**Alexander Baranov**

Affiliation:
Institute of Mathematics, Academy of Sciences of Belarus, Surganova 11, Minsk, 220072, Belarus

Email:
baranov@im.bas-net.by

**Alexander Kleshchev**

Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Email:
klesh@math.uoregon.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02003-6

Received by editor(s):
November 25, 1996

Additional Notes:
Supported by the Fundamental Research Foundation of Belarus and the National Science Foundation

Article copyright:
© Copyright 1999
American Mathematical Society