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Original Articles

Vertices of Low-Dimensional Simple Modules for Symmetric Groups

Pages 4521-4539 | Received 29 Jul 2007, Published online: 12 Dec 2008

REFERENCES

  • Benson , D. J. ( 1988 ). Spin modules for symmetric groups . J. London Math. Soc. 38 : 250 – 262 .
  • Bosma , W. , Cannon , J. , Playoust , C. ( 1997 ). The Magma algebra system. I. The user language . J. Symbolic Comput. 24 ( 3–4 ): 235 – 265 .
  • Brundan , J. , Kleshchev , A. (2001). Representations of the symmetric groups which are irreducible over subgroups. J. Reine Angew. Math. 530:145–190.
  • Brundan , J. , Kleshchev , A. ( 2003 ). Representation Theory of Symmetric Groups and their Double Covers . Groups, combinatorics and geometry (Durham, 2001) . River Edge , NJ : World Sci. Publishing , pp. 31 – 53 .
  • Danz , S. ( 2007a ). Theoretische und Algorithmische Methoden zur Berechnung von Vertizes Irreduzibler Moduln Symmetrischer Gruppen . Ph.D. thesis . University of Jena , Jena , Germany .
  • Danz , S. ( 2007b ). On vertices of exterior powers of the natural simple module for the symmetric group in odd characteristic . Arch. Math. 89 : 485 – 496 .
  • Danz , S. , Külshammer , B. , Zimmermann , R. ( 2008 ). On vertices of simple modules for symmetric groups of small degrees . J. Algebra 320 : 680 – 707 .
  • Donkin , S. ( 1987 ). On Schur algebras and related algebras II . J. Algebra 111 : 354 – 364 .
  • Grabmeier , J. ( 1985 ). Unzerlegbare Moduln mit Trivialer Youngquelle und Darstellungstheorie der Schuralgebra . Bayreuth. Math. Schr. 20 : 9 – 152 .
  • James , G. D. ( 1978 ). The Representation Theory of the Symmetric Groups . Berlin, Heidelberg, New York : Springer .
  • James , G. D. ( 1983a ). On the minimal dimensions of irreducible representations of symmetric groups . Math. Proc. Camb. Phil. Soc. 94 : 417 – 424 .
  • James , G. D. ( 1983b ). Trivial source modules for symmetric groups . Arch. Math. 41 : 294 – 300 .
  • James , G. D. , Kerber , A. ( 1981 ). The Representation Theory of the Symmetric Group . Encycl. Math. Appl. 16. Reading : Addison-Wesley .
  • Kleshchev , A. ( 2005 ). Linear and Projective Representations of Symmetric Groups . Cambridge : Cambridge University Press .
  • Knörr , R. ( 1979 ). On the vertices of irreducible modules . Ann. Math. 110 ( 2 ): 487 – 499 .
  • Külshammer , B. ( 1993 ). Some indecomposable modules and their vertices . J. Pure and Applied Algebra 86 : 65 – 73 .
  • Müller , J. , Zimmermann , R. ( 2007 ). Green vertices and sources of simple modules of the symmetric group . Arch. Math. 89 : 97 – 108 .
  • Peel , M. ( 1971 ). Hook representations of the symmetric groups . Glasgow Math. J. 12 : 136 – 149 .
  • Wales , D. B. ( 1979 ). Some projective representations of S n . J. Algebra 61 : 37 – 57 .
  • Wildon , M. ( 2003 ). Two theorems on the vertices of Specht modules . Arch. Math. 81 : 505 – 511 .
  • Zimmermann , R. ( 2004 ). Vertizes Einfacher Moduln der Symmetrischen Gruppen . Ph.D. thesis . University of Jena , Jena , Germany .
  • Communicated by A. Turull.

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