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Related Experiment Videos

Singular Integrals and the Principal Series, II.

A W Knapp1, E M Stein

  • 1CORNELL UNIVERSITY, ITHACA, NEW YORK.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 1970
PubMed
Summary

This study explores intertwining operators for simple Lie groups, extending findings from real rank one to higher ranks. Researchers analyzed the reducibility of principal series and the existence of complementary series.

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Area of Science:

  • Mathematics
  • Representation Theory
  • Group Theory

Background:

  • Intertwining operators are crucial for understanding representations of Lie groups.
  • Previous research focused on simple Lie groups of real rank one.

Purpose of the Study:

  • To extend the study of intertwining operators to higher rank simple Lie groups.
  • To investigate the reducibility of principal series representations.
  • To determine the existence of complementary series representations.

Main Methods:

  • Analysis of intertwining operators.
  • Extension of techniques from real rank one to higher ranks.
  • Investigating reducibility and complementary series properties.

Main Results:

  • Established results for intertwining operators in higher rank simple Lie groups.
  • Provided insights into the reducibility of principal series.
  • Demonstrated the existence of complementary series under certain conditions.

Conclusions:

  • The study successfully extended the analysis of intertwining operators to a broader class of Lie groups.
  • The findings contribute to the understanding of representation theory for higher rank simple Lie groups.

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