报告摘要： (Joint work with Junbin Dong)
The classification of all (abstract) irreducible representations of an reductive group G is a challenge problem and extremely difficult. In this talk, we will interested in the irreducible modules occurs in the abstract induced modules from an one dimensional modules of the Borel subgroup B. I will talk about my following recent work: Let k be a field and be a reductive group over . We show that the abstract induced module from an one dimensional representation of has a composition series if char k char . In the case and is a rational character, we give the necessary and sufficient condition for the existence of the composition series of . We determine all the composition factors whenever the composition series exist. The decomposition of such induced modules gives a large class of abstract infinite dimensional irreducible representations of G.