158 research outputs found

    Irreducible subgroups of algebraic groups

    Get PDF

    Irreducible subgroups of algebraic groups

    Get PDF
    A closed subgroup of a semisimple algebraic group G is said to be G‐irreducible if it lies in no proper parabolic subgroup of G. We prove a number of results concerning such subgroups. Firstly they have only finitely many overgroups in G; secondly, with some specified exceptions, there exist G‐irreducible subgroups of type A1; and thirdly, we prove an embedding theorem for G‐irreducible subgroup

    Multiplicity-free representations of algebraic groups II

    Full text link
    We continue our work (started in ``Multiplicity-free representations of algebraic groups", arXiv:2101.04476), on the program of classifying triples (X,Y,V)(X,Y,V), where X,YX,Y are simple algebraic groups over an algebraically closed field of characteristic zero with X<YX<Y, and VV is an irreducible module for YY such that the restriction VXV\downarrow X is multiplicity-free. In this paper we handle the case where XX is of type AA, and is irreducibly embedded in YY of type B,CB,C or DD. It turns out that there are relatively few triples for XX of arbitrary rank, but a number of interesting exceptional examples arise for small ranks.Comment: 60 page

    Rank 3 permutation characters and maximal subgroups

    Full text link
    In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a stabilizer of a point in E. This result has an application to the study of minimal genera of algebraic curves which admit group actions.Comment: 41 pages, to appear in Forum Mathematicu

    A Census Of Highly Symmetric Combinatorial Designs

    Full text link
    As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have remained longstanding challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of particular interest and has been open for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating back to 1965). The present paper continues the author's work [20, 21, 22] of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics
    corecore