Kyoto Journal of Mathematics

The moduli of representations of degree 2

Kazunori Nakamoto

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Abstract

There are six types of 2-dimensional representations in general. For any groups and any monoids, we can construct the moduli of 2-dimensional representations for each type: the moduli of absolutely irreducible representations, representations with Borel mold, representations with semisimple mold, representations with unipotent mold, representations with unipotent mold over F2, and representations with scalar mold. We can also construct them for any associative algebras.

Article information

Source
Kyoto J. Math., Volume 57, Number 4 (2017), 829-902.

Dates
Received: 13 May 2014
Revised: 8 June 2016
Accepted: 13 July 2016
First available in Project Euclid: 16 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1497600015

Digital Object Identifier
doi:10.1215/21562261-2017-0017

Mathematical Reviews number (MathSciNet)
MR3725262

Zentralblatt MATH identifier
06825579

Subjects
Primary: 14D22: Fine and coarse moduli spaces
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 20M30: Representation of semigroups; actions of semigroups on sets 20C99: None of the above, but in this section 16G99: None of the above, but in this section

Keywords
moduli of representations 2-dimensional representations representation variety character variety mold

Citation

Nakamoto, Kazunori. The moduli of representations of degree $2$. Kyoto J. Math. 57 (2017), no. 4, 829--902. doi:10.1215/21562261-2017-0017. https://projecteuclid.org/euclid.kjm/1497600015


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References

  • [1] S. Cavazos and S. Lawton,$E$-polynomial of $\operatorname{SL}_{2}({\mathbb{C}})$-character varieties of free groups, Internat. J. Math.25(2014), no. 1450058.
  • [2] A. Grothendieck and J. Dieudonné,Éléments de géométrie algébrique, I: Le langage des schémas, Publ. Math. Inst. Hautes Études Sci.4(1960).
  • [3] A. Grothendieck,Éléments de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents, I, Publ. Math. Inst. Hautes Études Sci.11(1961).
  • [4] A. Grothendieck,Éléments de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas, II, Publ. Math. Inst. Hautes Études Sci.24(1965).
  • [5] A. Grothendieck,Éléments de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas, III, Publ. Math. Inst. Hautes Études Sci.28(1966).
  • [6] R. Hartshorne,Algebraic Geometry, Grad. Texts in Math.52, Springer, New York, 1977.
  • [7] S. Lawton and V. Muñoz,$E$-polynomial of the $\operatorname{SL}({3},{\mathbb{C}})$-character variety of free groups, Pacific J. Math.282(2016), 173–202.
  • [8] J. S. Milne,Étale Cohomology, Princeton Math. Ser.33, Princeton Univ. Press, Princeton, 1980.
  • [9] D. Mumford, J. Fogarty, and F. Kirwan,Geometric Invariant Theory, 3rd ed., Ergeb. Math. Grenzgeb. (2)34, Springer, Berlin, 1994.
  • [10] K. Nakamoto,Representation varieties and character varieties, Publ. Res. Inst. Math. Sci.36(2000), 159–189.
  • [11] K. Nakamoto,The structure of the invariant ring of two matrices of degree $3$, J. Pure Appl. Algebra166(2002), 125–148.
  • [12] K. Nakamoto,The moduli of representations with Borel mold, Internat. J. Math.25(2014), no. 1450067.
  • [13] K. Nakamoto and T. Torii,Virtual Hodge polynomials of the moduli spaces of representations of degree $2$ for free monoids, Kodai Math. J.39(2016), 80–109.
  • [14] M. Reineke,Counting rational points of quiver moduli, Int. Math. Res. Not. IMRN2006, art. ID 70456.
  • [15] K. Saito,Representation varieties of a finitely generated group into $\operatorname{SL}_{2}$ or $\operatorname{GL}_{2}$, RIMS preprint, RIMS-958, 1993.
  • [16] K. Saito, “Character variety of representations of a finitely generated group in $\operatorname{SL}_{2}$” inTopology and Teichmüller Spaces (Katinkulta, 1995), World Sci., River Edge, N.J., 1996, 253–264.