Modality of Representations, and Packets for θ-Groups
We first establish several general properties of modality of algebraic group actions. In particular,we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we classify irreducible linear representations of connected simple algebraic groups of every fixed modality ≤ 2. Next, exploring a finer geometric structure of linear actions, we generalize to the case of any cyclically graded semisimple Lie algebra the notion of a packet (or a Jordan/decomposition class) and establish the properties of packets.
KeywordsAlgebraic group action Modality θ-group Packet Sheet
Mathematics Subject Classification (2010):14L30 (Primary) 20G05
Unable to display preview. Download preview PDF.