Modality of Representations, and Packets for θ-Groups

  • Vladimir L. PopovEmail author
Part of the Progress in Mathematics book series (PM, volume 326)


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.


Algebraic group action Modality θ-group Packet Sheet 

Mathematics Subject Classification (2010):

14L30 (Primary) 20G05 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesGubkina 8Russia
  2. 2.Russia and National Research UniversityHigher School of EconomicsMoscowRussia

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