Tensor representations of the general linear super group

  • Rita Fioresi


We show a correspondence between tensor representations of the super general linear group GL(m|n) and tensor representations of the general linear superalgebra gl(m|n) using a functorial approach.


Irreducible Representation Young Tableau Tensor Representation Representable Functor Hopf Superalgebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    [1] F. A. Berezin, Introction to superanalysis. Edited by A. A. Kirillov. D. Reideldu Publishing Company, Dordrecht (Holland) (1987).Google Scholar
  2. [2]
    [2] A. Baha Balantekin, I. Bars Dimension and character formula for Lie supergroups, J. Math. Phy., 22, 1149–1162, (1981).MATHCrossRefGoogle Scholar
  3. [3]
    [3] A. Berele, A. Regev Hook Young Diagrams with applications to combinatorics and to representations of Lie superalgebras, Adv. Math., 64, 118–175, (1987).MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    [4] A. Brini, F. Regonati, A. Teolis The method of virtual variables and representations of Lie superalgebras. Clifford algebras (Cookeville, TN, 2002), 245–263, Prog. Math. Phys., 34, Birkhauser Boston, MA, (2004). Combinatorics and representation theory of Lie superalgebras over letterplace superalgebras. Li, Hongbo (ed.) et al., Computer algebra and geometric algebra with applications. 6th international workshop, IWMM 2004, Shanghai, China, Berlin: Springer. Lecture Notes in Computer Science 3519, 239–257 (2005).Google Scholar
  5. [5]
    [5] L. Caston, R. Fioresi, Mathematical Foundations of Supersymmetry,, 0710.5742v1, 2007.Google Scholar
  6. [6]
    [6] P. Deligne and J. Morgan, Notes on supersymmetry (following J. Bernstein), in “Quantum fields and strings. A course for mathematicians”, Vol 1, AMS, (1999).Google Scholar
  7. [7]
    [7] P. H. Dondi, P. D. Jarvis Diagram and superfields tecniques in the classical superalgebras, J. Phys. A, Math. Gen 14, 547–563, (1981).MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    [8] R. Fioresi, M. A. Lledo On Algebraic Supergroups, Coadjoint Orbits and their Deformations, Comm. Math. Phy. 245, no. 1, 177–200, (2004).MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    [9] R. Fioresi, On algebraic supergroups and quantum deformations, math.QA/0111113, J. Algebra Appl. 2, no. 4, 403–423, (2003).MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    [10] R. Fioresi, Supergroups, quantum supergroups and their homogeneous spaces. Euroconference on Brane New World and Noncommutative Geometry (Torino, 2000). Modern Phys. Lett. A 16 269–274 (2001).CrossRefMathSciNetGoogle Scholar
  11. [11]
    [11] G. James, A. Kerber The representation theory of the symmetric group, Encyclopedia of Mathematics and its applications Vol. 16, Addison Wesley, (1981).Google Scholar
  12. [12]
    [12] V. Kac Lie superalgebras Adv. in Math. 26, 8–26, (1977).MATHCrossRefGoogle Scholar
  13. [13]
    [13] B. Kostant, Graded manifolds, Graded Lie theory and prequantization. Lecture Notes in Math. 570 (1977).Google Scholar
  14. [14]
    [14] D. A. Leites, Introduction to the theory of supermanifolds. Russian Math. Survey. 35:11–64 (1980).CrossRefMathSciNetGoogle Scholar
  15. [15]
    [15] Yu. Manin, Gauge field theory and complex geometry. Springer Verlag, (1988).Google Scholar
  16. [16]
    [16] Yu. Manin, Topics in non commutative geometry. Princeton University Press, (1991).Google Scholar
  17. [17]
    [17] A. N. Sergeev The tensor algebra of the identity representation as a module over the Lie superalgebras gl(m|n) and Q(n), Math. USSR Sbornik, 51, no. 2, (1985).Google Scholar
  18. [18]
    [18] M. Scheunert, R. B. Zhang The general linear supergroup and its Hopf superalgebra of regular functions, J. Algebra 254, no. 1, 44–83, (2002).MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    [19] V. S. Varadarajan Supersymmetry for mathematicians: an Introduction, AMS, (2004).Google Scholar

Copyright information

© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2011

Authors and Affiliations

  • Rita Fioresi
    • 1
  1. 1.Dipartimento di MatematicaUniversitá di BolognaBolognaItaly

Personalised recommendations