Algebras and Representation Theory

, Volume 18, Issue 5, pp 1357–1388 | Cite as

The Blocks of the Partition Algebra in Positive Characteristic

  • C. Bowman
  • M. De Visscher
  • O. King


In this paper we describe the blocks of the partition algebra over a field of positive characteristic.


Partition algebra Blocks 

Mathematics Subject Classification (2010)



  1. 1.
    Cox, A.G., De Visscher, M., Doty, S., Martin, P.: On the blocks of the walled Brauer algebra. J. Algebra 320, 169–212 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Cox, A.G., De Visscher, M., Martin, P.P.: The blocks of the Brauer algebra in characteristic zero. Represent. Theory 13, 272–308 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Cox, A., De Visscher, M., Martin, P.: A geometric characterisation of the blocks of the Brauer algebra. J. London Math. Soc. 80, 471–494 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Doran, W.F., Wales, D.B.: The partition algebra revisited. J. Algebra 231, 265–330 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Enyang, J.: A seminormal form for partition algebras. J. Comb. Theory Ser. A 120, 1737–1785 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Graham, J.J., Lehrer, G.I.: Cellular algebras, Invent. Math 123, 1–34 (1996)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Green, J.A.: Polynomial representations of G L n, Lecture Notes in Mathematics, vol. 830. Springer (1980)Google Scholar
  8. 8.
    Hartmann, R., Henke, A., König, S., Paget, R.: Cohomological stratification of diagram algebras. Math. Ann. 347, 765–804 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Halverson, T., Ram, A.: Partition algebras, European. J. Combin. 26, 869–921 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    James, G.D.: The representation theory of the symmetric groups, Lecture Notes in Mathematics, vol. 682. Springer-Verlag (1978)Google Scholar
  11. 11.
    James, G.D., Kerber, A.: The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16. Addison-Wesley (1981)Google Scholar
  12. 12.
    MacDonald, I.G.: Symmetric functions and Hall polynomials, Oxford Mathematical Monographs. Oxford University Press (1995)Google Scholar
  13. 13.
    Martin, P.: Potts models and related problems in statistical mechanics, Series on Advances in Statistical Mechanics, vol. 5. World Scientific Publishing Co., Inc., Teaneck, NJ (1991). MR 1103994 (92m:82030)CrossRefGoogle Scholar
  14. 14.
    Martin, P.P.: The structure of the partition algebras. J. Algebra 183, 319–358 (1996)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Martin, P.P.: The partition algebra and the potts model transfer matrix spectrum in high dimensions. J. Phys. A 33(19), 3669–3695 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Mathas, A.: Iwahori-hecke algebras and schur algebras of the symmetric groupGoogle Scholar
  17. 17.
    Xi, C.: Partition algebras are cellular. Compos. Math. 119, 107–118 (1999)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of MathematicsCity University London, Northampton SquareLondonEngland

Personalised recommendations