Representation Of Semisimple Algebraic Group Research Articles

Invariants of algebraic group actions from differential point of view

In this paper we suggest an approach to study actions of semisimple (or reductive) algebraic groups in their algebraic complex representations. We use differential-geometric methods instead of classical algebraic constructions. Namely, according to Borel–Weil–Bott theorem, every algebraic representation of semisimple algebraic group is isomorphic to the action of this group on the module of holomorphic sections of some reductive bundle over homogeneous space. Using this, we give a complete description of the field of differential invariants for this action and obtain a criterion, which separates regular orbits.

Irreducible representations of semisimple algebraic groups and supersolvable lattices

Let Λ be the cross section lattice of an irreducible representation of a semisimple algebraic group. Certain combinatorial properties of Λ are studied. Supersolvable Λʼs are determined in terms of Dynkin diagrams. The characteristic polynomial of a supersolvable Λ is computed.

On restrictions of Irreducible Modular Representations of Semisimple Algebraic Groups and Symmetric Groups to Some Natural Subgroups, I

(1994). On restrictions of irreducible modular representations of semisimple algebraic groups and symmetric groups to some natural subgroups, II. Communications in Algebra: Vol. 22, No. 15, pp. 6175-6208.

On restrictions of irreducible modular representations of semisimple algebraic groups and symmetric groups to some natural subgroups, II

On restrictions of irreducible modular representations of semisimple algebraic groups and symmetric groups to some natural subgroups, II

On certain representations of semi-simple algebraic groups and the arithmetic of the corresponding invariants (1)

On certain representations of semi-simple algebraic groups and the arithmetic of the corresponding invariants (1)

Representations of Algebraic Groups

Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the representations of corresponding finite simple groups. (Each algebraic group is assumed to be defined over a universal field which is algebraically closed and of infinite degree of transcendence over the prime field, and all of its representations are assumed to take place on vector spaces over this field.)