Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 29
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Fawcett, Joanna B. O'Brien, E.A. and Saxl, Jan 2016. Regular orbits of symmetric and alternating groups. Journal of Algebra, Vol. 458, p. 21.


    Müller, Jürgen 2016. On low-degree representations of the symmetric group. Journal of Algebra,


    GLASBY, S. P. LÜBECK, FRANK NIEMEYER, ALICE C. and PRAEGER, CHERYL E. 2015. PRIMITIVE PRIME DIVISORS AND THE TH CYCLOTOMIC POLYNOMIAL. Journal of the Australian Mathematical Society, p. 1.


    Levaillant, Claire 2015. Classification of the Invariant Subspaces of the Cohen–Wales Representation of the Artin Group of TypeDn: Table 1.. International Mathematics Research Notices, Vol. 2015, Issue. 21, p. 11253.


    Baranov, A.A. Osinovskaya, A.A. and Suprunenko, I.D. 2014. Modular representations of the special linear groups with small weight multiplicities. Journal of Algebra, Vol. 397, p. 225.


    Burness, Timothy C. Guralnick, Robert M. and Saxl, Jan 2014. Base sizes for S-actions of finite classical groups. Israel Journal of Mathematics, Vol. 199, Issue. 2, p. 711.


    Häsä, Jokke 2014. Growth of cross-characteristic representations of finite quasisimple groups of Lie type. Journal of Algebra, Vol. 407, p. 275.


    Tiep, Pham Huu 2014. Representation of finite groups: conjectures, reductions, and applications. Acta Mathematica Vietnamica, Vol. 39, Issue. 1, p. 87.


    Tong-Viet, Hung P. 2013. Rank 3 permutation characters and maximal subgroups. Forum Mathematicum, Vol. 25, Issue. 1,


    Dong, HuiLi and Zhou, ShengLin 2012. Affine groups and flag-transitive triplanes. Science China Mathematics, Vol. 55, Issue. 12, p. 2557.


    Kleshchev, Alexander S. and Tiep, Pham Huu 2012. Small-dimensional projective representations of symmetric and alternating groups. Algebra & Number Theory, Vol. 6, Issue. 8, p. 1773.


    LEVAILLANT, CLAIRE 2012. REDUCIBILITY OF THE COHEN–WALES REPRESENTATION OF THE ARTIN GROUP OF TYPE Dn. Journal of Knot Theory and Its Ramifications, Vol. 21, Issue. 10, p. 1250071.


    THOMAS, SIMON and ZAPLETAL, JINDŘICH 2012. ON THE STEINHAUS AND BERGMAN PROPERTIES FOR INFINITE PRODUCTS OF FINITE GROUPS. Confluentes Mathematici, Vol. 04, Issue. 02, p. 1250002.


    Tong-Viet, Hung P. 2012. Alternating and Sporadic Simple Groups are Determined by Their Character Degrees. Algebras and Representation Theory, Vol. 15, Issue. 2, p. 379.


    Levaillant, Claire and Wales, David 2010. Parameters for which the Lawrence–Krammer representation is reducible. Journal of Algebra, Vol. 323, Issue. 7, p. 1966.


    Levaillant, Claire 2009. Irreducibility of the Lawrence–Krammer representation of the BMW algebra of type. Comptes Rendus Mathematique, Vol. 347, Issue. 1-2, p. 15.


    Bessenrodt, Christine and Weber, Heike 2008. On p-blocks of symmetric and alternating groups with all irreducible Brauer characters of prime power degree. Journal of Algebra, Vol. 320, Issue. 6, p. 2405.


    Danz, Susanne 2008. Vertices of Low-Dimensional Simple Modules for Symmetric Groups. Communications in Algebra, Vol. 36, Issue. 12, p. 4521.


    Liebeck, Martin W. Pyber, Laszlo and Shalev, Aner 2007. On a conjecture of G.E. Wall. Journal of Algebra, Vol. 317, Issue. 1, p. 184.


    van Bon, John 2007. Finite primitive distance-transitive graphs. European Journal of Combinatorics, Vol. 28, Issue. 2, p. 517.


    ×
  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 94, Issue 3
  • November 1983, pp. 417-424

On the minimal dimensions of irreducible representations of symmetric groups

  • G. D. James (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100000803
  • Published online: 24 October 2008
Abstract

For each integer m, Rasala [6] has shown how to list all the ordinary irreducible representations of the symmetric group n which have degree less than nm, provided that n is large enough, and in this note we shall prove similar results for the irreducible representations of n over an arbitrary field K. Our estimates are very crude, so although we recover Rasala's results, we get nowhere near his precise information on how large n has to be.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] G. D. James . The Representation Theory of the Symmetric Groups. Lecture Notes in Math. vol. 682 (Springer-Verlag, 1978).

[2] G. D. James . Representations of the symmetric groups over the field of order 2. J. Algebra 38 (1976), 280308.

(3)G. D. James . On the decomposition matrices of the symmetric groups II. J. Algebra 43 (1977), 4554.

[4] G. D. James . On the decomposition matrices of the symmetric groups III. J. Algebra 71 (1981), 115122.

[6] R. Rasala . On the minimal degrees of characters of Sn. J. Algebra 45 (1977), 132181.

[7] A. Wagner . The faithful linear representations of least degree of Sn and An over a field of characteristic 2. Math. Zeit. 151 (1976), 127137.

[8] A. Wagner . The faithful linear representations of least degree of Sn and An over a field of odd characteristic. Math. Zeit. 154 (1977), 103114.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×