Skip to main content
SpringerLink
Log in

On representation varieties of free abelian groups

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

The reducibility of the representation variety of a free abelian group of finite rank in a semisimple non-simply connected algebraic group is proved. Irreducible components of the representation variety of a free abelian group of rank 2 in groups of type A n are described.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Lubotzky and A. R. Magid, Varieties of Representations of Finitely Generated Groups (Am. Math. Soc., Providence, RI, 1985), Mem. AMS 58 (336).

    MATH  Google Scholar 

  2. V. P. Platonov and A. S. Rapinchuk, Algebraic Groups and Number Theory (Nauka, Moscow, 1991; Academic, Boston, MA, 1994).

    MATH  Google Scholar 

  3. R. W. Richardson, “Commuting varieties of semisimple Lie algebras and algebraic groups,” Compos. Math. 38 (3), 311–327 (1979).

    MathSciNet  MATH  Google Scholar 

  4. A. A. Sharomet, “On the variety of pairs of commuting matrices of a non-simply-connected algebraic group,” in XI Belarus. Math. Conf.: Abstracts of Talks (Inst. Mat., Nats. Akad. Navuk Belarusi, Minsk, 2012), Part 5, pp. 57–58.

    Google Scholar 

  5. A. S. Rapinchuk, V. V. Benyash-Krivetz, and V. I. Chernousov, “Representation varieties of the fundamental groups of compact orientable surfaces,” Isr. J. Math. 93, 29–71 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  6. T. S. Motskin and O. Taussky, “Pairs of matrices with property L. II,” Trans. Am. Math. Soc. 80, 387–401 (1955).

    MathSciNet  MATH  Google Scholar 

  7. R. Guralnick, “A note on commuting pairs of matrices,” Linear Multilinear Algebra 31 (1–4), 71–75 (1992).

  8. K. Šivic, “On varieties of commuting triples. III,” Linear Algebra Appl. 437 (2), 393–460 (2012).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belarusian State University, Nezavisimosti Ave. 4, Minsk, 220030, Belarus

    A. A. Sharomet

Authors
  1. A. A. Sharomet
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Sharomet.

Additional information

Original Russian Text © A.A. Sharomet, 2016, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 292, pp. 255–263.

To V.P. Platonov on his 75th birthday

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sharomet, A.A. On representation varieties of free abelian groups. Proc. Steklov Inst. Math. 292, 247–255 (2016). https://doi.org/10.1134/S0081543816010156

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543816010156

Keywords

Search

Navigation