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Property (T) for groups graded by root systems / Mikhail Ershov, Andrei Jaikin-Zapirain and Martin Kassabov.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 249, no 1186.Publication details: Providence : American Mathematical Society, 2017.Description: v, 135 pages : illustrations ; 26 cmISBN:
  • 9781470426040 (alk. paper)
Other title:
  • Property for groups graded by root systems
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Generalized spectral criterion -- Chapter 4. Root Systems -- Chapter 5. Property $(T)$ for groups graded by root systems -- Chapter 6. Reductions of root systems -- Chapter 7. Steinberg groups over commutative rings -- Chapter 8. Twisted Steinberg groups -- Chapter 9. Application: Mother group with property $(T)$ -- Chapter 10. Estimating relative Kazhdan constants -- Appendix A. Relative property $(T)$ for $(\mathrm St_n(R)\ltimes R^n,R^n)$.
Summary: Introduces and studies the class of groups graded by root systems. The authors prove that if $\Phi$ is an irreducible classical root system of rank $\geq 2$ and $G$ is a group graded by $\Phi$, then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of $G$.
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Includes bibliographical references and index.

Chapter 1. Introduction --
Chapter 2. Preliminaries --
Chapter 3. Generalized spectral criterion --
Chapter 4. Root Systems --
Chapter 5. Property $(T)$ for groups graded by root systems --
Chapter 6. Reductions of root systems --
Chapter 7. Steinberg groups over commutative rings --
Chapter 8. Twisted Steinberg groups --
Chapter 9. Application: Mother group with property $(T)$ --
Chapter 10. Estimating relative Kazhdan constants --
Appendix A. Relative property $(T)$ for $(\mathrm St_n(R)\ltimes R^n,R^n)$.

Introduces and studies the class of groups graded by root systems. The authors prove that if $\Phi$ is an irreducible classical root system of rank $\geq 2$ and $G$ is a group graded by $\Phi$, then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of $G$.

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