ON LATTICES OF INTEGRAL GROUP ALGEBRAS AND SOLOMON ZETA FUNCTIONS
We investigate integral forms of certain simple modules over group algebras in characteristic 0 whose
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- C. Bonnafé, Representations of SL2(Fq), Algebra and Applications, 13,
Springer-Verlag London, Ltd., London, 2011.
- C. J. Bushnell and I. Reiner, Solomon’s conjectures and the local functional
equation for zeta functions of orders, Bull. Amer. Math. Soc. (N.S.), 2(2)
(1980), 306-310.
- M. Craig, A characterization of certain extreme forms, Illinois J. Math., 20(4)
(1976), 706-717.
- C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. I. With
applications to finite groups and orders, Pure and Applied Mathematics, A
Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1981.
- S. Danz and T. Hofmann, On integral forms of Specht modules labelled by hook
partitions, Preprint, arXiv:1706.02860v2, (2018).
- T. Hofmann, Zeta functions of lattices of the symmetric group, Comm. Algebra,
44(5) (2016), 2243-2255.
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften,
Band 134, Springer-Verlag, Berlin-New York, 1967.
- G. D. James, The irreducible representations of the symmetric groups, Bull.
London Math. Soc., 8(3) (1976), 229-232.
- G. D. James, The Representation Theory of the Symmetric Groups, Lecture
Notes in Mathematics, 682, Springer, Berlin, 1978.
- G. D. James, Representations of General Linear Groups, London Mathematical
Society Lecture Note Series, 94, Cambridge University Press, Cambridge, 1984.
- J. Müller and J. Orlob, On the structure of the tensor square of the natural
module of the symmetric group, Algebra Colloq., 18(4) (2011), 589-610.
- W. Plesken, Beiträge zur Bestimmung der endlichen irreduziblen Untergruppen
von GL(n,Z) und ihrer ganzzahligen Darstellungen. PhD thesis, RWTH
Aachen, 1974.
- W. Plesken, On absolutely irreducible representations of orders, In Hans
Zassenhaus, editor, Number theory and algebra, Academic Press, New York,
(1977), 241-262.
- W. Plesken, Gruppenringe über lokalen Dedekindbereichen, Habilitation,
RWTH Aachen, 1980.
- W. Plesken, Group Rings of Finite Groups over p-adic Integers, Lecture Notes
in Mathematics, 1026, Springer-Verlag, Berlin, 1983.
- L. Solomon, Zeta functions and integral representation theory, Advances in
Math., 26(3) (1977), 306-326.