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Regular version of the site

Book chapter

Modality of representations and geometry of θ-groups

P. 459-479.

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 < 3. 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.