Overgroups of irreducible linear groups, II
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Abstract:
Determining the subgroup structure of algebraic groups (over an algebraically closed field $K$ of arbitrary characteristic) often requires an understanding of those instances when a group $Y$ and a closed subgroup $G$ both act irreducibly on some module $V$, which is rational for $G$ and $Y$. In this paper and in Overgroups of irreducible linear groups, I (J. Algebra 181 (1996), 26–69), we give a classification of all such triples $(G,Y,V)$ when $G$ is a non-connected algebraic group with simple identity component $X$, $V$ is an irreducible $G$-module with restricted $X$-high weight(s), and $Y$ is a simple algebraic group of classical type over $K$ sitting strictly between $X$ and $\operatorname {SL}(V)$.References
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Additional Information
- Ben Ford
- Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
- Address at time of publication: Department of Mathematics, Sonoma State University, Rohnert Park, California 94928
- MR Author ID: 360279
- Email: ben.ford@sonoma.edu
- Received by editor(s): August 18, 1995
- Received by editor(s) in revised form: April 30, 1997
- Published electronically: May 3, 1999
- Additional Notes: Supported in part by the NSF and the NSA
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 3869-3913
- MSC (1991): Primary 20G05
- DOI: https://doi.org/10.1090/S0002-9947-99-02138-8
- MathSciNet review: 1467464