Integral representations for the alternating groups
HTML articles powered by AMS MathViewer
- by Udo Riese
- Proc. Amer. Math. Soc. 130 (2002), 3515-3518
- DOI: https://doi.org/10.1090/S0002-9939-02-06518-8
- Published electronically: May 1, 2002
- PDF | Request permission
Abstract:
We show that every complex representation of an alternating group can be realized over the ring of integers of a “small” abelian number field.References
- Gerald Cliff, Jürgen Ritter, and Alfred Weiss, Group representations and integrality, J. Reine Angew. Math. 426 (1992), 193–202. MR 1155753
- Franz Rádl, Über die Teilbarkeitsbedingungen bei den gewöhnlichen Differential polynomen, Math. Z. 45 (1939), 429–446 (German). MR 82, DOI 10.1007/BF01580293
- Gordon James and Adalbert Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley Publishing Co., Reading, Mass., 1981. With a foreword by P. M. Cohn; With an introduction by Gilbert de B. Robinson. MR 644144
- Wolfgang Knapp and Peter Schmid, An extension theorem for integral representations, J. Austral. Math. Soc. Ser. A 63 (1997), no. 1, 1–15. MR 1456586
- Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
- U. Riese, On integral representations for SL$(2,q)$, J. Algebra 242 (2001), 729–739.
- Udo Riese and Peter Schmid, Schur indices and Schur groups. II, J. Algebra 182 (1996), no. 1, 183–200. MR 1388863, DOI 10.1006/jabr.1996.0167
- Fumiyuki Terada, A principal ideal theorem in the genus field, Tohoku Math. J. (2) 23 (1971), 697–718. MR 306158, DOI 10.2748/tmj/1178242555
Bibliographic Information
- Udo Riese
- Affiliation: Universität Tübingen, Mathematisches Institut, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
- Email: udo.riese@uni-tuebingen.de
- Received by editor(s): May 3, 2001
- Received by editor(s) in revised form: July 30, 2001
- Published electronically: May 1, 2002
- Communicated by: Stephen D. Smith
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3515-3518
- MSC (2000): Primary 20C10, 20C30
- DOI: https://doi.org/10.1090/S0002-9939-02-06518-8
- MathSciNet review: 1918827