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In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a represen
In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation (\rho, V) or irrep of an algebraic structure A is a nonzero
In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs bot
For G a simple algebraic group over an algebraically closed field of characteristic 0, we determine the irreducible representations ρ:G→I(V), where I(V) denotes one of the classical groups SL(V), Sp(V), SO(V), such that ρ sends some distinguished unipotent element of G to a distinguished element of I(V). We also settle a base case of the general problem of determining when the restriction of ρ to a simple subgroup of G is multiplicity-free.
Let G be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field F of characteristic p >= 0, and let u is an element of G be a non-identity unipotent element. Let phi be a non-trivial irreducible representation of G. Then the Jordan normal form of phi(u) contains at most one non-trivial block if and only if G is of type G(2), u is a regular unipotent element and dim phi
2018
Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple linear algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of independent interest. In particular, we determine the irreducible representations of simple algebraic groups whose non-zero weights occur with multiplicity 1.