Elementary Divisors of Gram Matrices of Certain Specht Modules

References

• Bennett , M. A. 1998 . On the number of solutions of simultaneous Pell equations . J. Reine Angew. Math. , 498 : 173 – 199 .
   Google Scholar
• Benson , D. J. 1987 . Some remarks on the decomposition numbers for the symmetric groups . Proc. Sympos. Pure Math. , 47 : 381 – 394 .
   Google Scholar
• Carter , R. W. and Payne , M. T. J. 1980 . On homomorphisms between Weyl modules and Specht modules . Math. Proc. Cambridge Philos. Soc. , 87 : 419 – 425 .
   Google Scholar
• Fayers , M. 2003 . On the structure of Specht modules . J. Lond. Math. Soc. , 67 ( 2 ) : 85 – 102 .
   Google Scholar
• Grabmeier , J. 1985 . Unzerlegbare Moduln mit trivialer Youngquelle und Darstellungstheorie der Schuralgebra . Bayreuth Math. Schr. , 20 : 9 – 152 .
   Google Scholar
• James , G. D. 1976 . On the decomposition matrices of the symmetric groups II . J. Algebra , 43 : 45 – 54 .
   Google Scholar
• James,G. D. (1978). The Representation Theory of the Symmetric Groups. SLN 682
   Google Scholar
• James , G. D. 1981 . On the decomposition matrices of the symmetric groups III . J. Algebra , 71 : 115 – 122 .
   Google Scholar
• James , G. D. and Kerber , A. 1981 . The Representation Theory of the Symmetric Group Addison-Wesley .
   Google Scholar
• James , G. D. and Murphy , G. E. 1979 . The determinant of the Gram matrix for a Specht module . J. Algebra , 59 : 222 – 235 .
   Google Scholar
• James , G. D. and Williams , A. 2000 . Decomposition numbers of symmetric groups by induction . J. Algebra , 228 : 119 – 142 .
   Google Scholar
• Kleshchev , A. S. 1995 . Branching rules for modular representations of symmetric groups II . J. Reine Angew. Math. , 459 : 163 – 212 .
   Google Scholar
• Kleshchev , A. S. and Sheth , J. 1999 . On extensions of simple modules over symmetric and algebraic groups . J. Algebra , 221 : 705 – 722 .
   Google Scholar
• Künzer,M. (1999). Ties for the Integral Group Ring of the Symmetric Group. Thesis,http://www.mathematik.uni-bielefeld.de/∼kuenzer,Bielefeld
   Google Scholar
• Künzer , M. A two-box-shift morphism between Specht modules,xxx-archive math.RT/0003083
   Google Scholar
• Lübeck , F. Elementary Divisors of Gram Matrices for Specht Modules of Symmetric Groups and Jantzen Filtrations,web page,http://www.math.rwth-aachen.de/∼ Frank.Luebeck/SpechtGram,Aachen
   Google Scholar
• Mathas , A. 1999 . Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group , Lecture Series Vol. 15 , AMS University .
   Google Scholar
• Mathieu , O. 1996 . On the dimension of some modular irreducible representations of the symmetric group . Lett. Math. Phys. , 38 ( 1 ) : 23 – 32 .
   Google Scholar
• Müller , J. 2000a . The 2-modular decomposition matrices of the symmetric groups 𝒮15,𝒮16,and 𝒮17 . Comm. Algebra , 28 ( 10 ) : 4997 – 5005 .
   Google Scholar
• Müller , J. 2000b . The 2-modular decomposition matrix of the symmetric group 𝒮18 (up to one ambiguity),Manuscript
   Google Scholar
• Müller , J. , Wilson , R. , Röhr , F. , Parker , R. , Ottensmann , M. , Lux , K. , Lübeck , F. , Jansen , C. , Hiß , G. and Brueur , T. 2000 . Decomposition Matrices,web page of the Atlas project,http://www.math.rwth-aachen.de/LDFM/homes/MOC/decomposition/,Aachen
   Google Scholar
• Nebe , G. 1999 . Orthogonale Darstellungen endlicher Gruppen und Gruppenringe,Habilitationsschrift,Aachen
   Google Scholar
• Peel , M. H. 1971 . Hook representation of the symmetric groups . Glasgow Math. J. , 12 : 136 – 149 .
   Google Scholar
• Plesken , W. 1980 . Gruppenringe über lokalen Dedekindbereichen,Habilitationsschrift,Aachen
   Google Scholar
• Plesken , W. 1983 . Group Rings of Finite Groups over p-adic Integers. SLN 1026
   Google Scholar
• Plesken , W. 1993 . Some arithmetic-geometric problems related to Specht-lattices . Bayreuth. Math. Schr. , 43 : 97 – 108 .
   Google Scholar
• Reuter , A. 2001 . The Submodule Structure of Specht Modules. Thesis,http://www.ma.ic.ac.uk/ ∼ ar598/research.html
   Google Scholar
• 1994 . Rosenberg J. (1994) Algebraic K-theory and Its Applications GTM 147,Springer
   Google Scholar
• Schaper , K. D. 1981 . Charakterformeln für Weyl-Moduln und Specht-Moduln in Primcharakteristik . Diplomarbeit,Bonn
   Google Scholar
• Sukhov , Yu. Yu. 1983 . On the question of determining the elements of decomposition matrices of symmetric groups . Mat. Zametki , 33 ( 6 ) : 819 – 822 .
   Google Scholar
• To Law K. W. Results on Decomposition Matrices for the Symmetric Groups (1983) Ph.D. thesis,University of Cambridge
   Google Scholar
• Wirsing E. (2002) Doch noch die ganze Antwort,letter to the authors
   Google Scholar
• Weil , A. 1992 . Zahlentheorie – Ein Gang durch die Geschichte von Hammurapi bis Legendre Birkhäuser .
   Google Scholar