Branching of Modular Representations of the Alternating Groups

Maximal Ideals in Modular Group Algebras of the Finitary Symmetric and Alternating Groups

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 p of the ground field is greater than 2). For the symmetric group there are exactly p − 1 such ideals and for the alternating group there are (p − 1)/2 of them. The description is obtained in terms of the annihilators of ...

Multiplying Modular Forms

The space of elliptic modular forms of fixed weight and level can be identified with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying elliptic modular forms corresponds to a branching problem involving tensor products of holomorphic discrete series representations. In this paper, we explicitly c...

Branching Rules for Modular Representations of Symmetric Groups, Iv

Branching Rules for Modular Fundamental Representations of Symplectic Groups

In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group Sp2n(K) to the naturally embedded subgroup Sp2n−2(K) is determined. As a corollary, inductive systems of fundamental representations for Sp∞(K) are classified. The submodule structure...

Asymptotic Results on Modular Representations of Symmetric Groups and Almost Simple Modular Group Algebras

In fact, this is a question about infinite simple groups because it is easy for G finite, and because a non-trivial normal subgroup gives rise to a non-trivial ideal different from the augmentation ideal. Also note that the problem reduces easily to the question on when the augmentation ideal is simple as a ring. The first interesting class of groups with almost simple FG was discovered in [3]....