Abstract
Combinatorial methods are presented for calculating the Fischer matrices of the generalized symmetric group and one of its covering groups.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.O. Almestady, Fischer matrices for generalized symmetric groups - a combi-natorial approach, Ph.D. thesis, University of Wales, Aberystwyth (1998).
M.O. Almestady, A.O.Morris, Fischer matrices for generalized symmetric groups - a combinatorial approach, (to appear).
M.O. Almestady, A.O.Morris, Fischer matrices for projective representations of generalized symmetric groups, (to appear).
J.W. Davies, A.O.Morris, The Schur multiplier of the generalized symmetric group, J. London Math. Soc. (2) 8 (1974), 615–620.
B. Fischer, Clifford Matrizen, (unpublished) (1976).
B. Fischer, Clifford matrices in Representation theory of finite groups and finite dimensional algebras, G.O. Michler and C.M. Ringel(eds), Progress in Mathematics Vol. 95, Birkhauser,Basel,(1991), 1–16.
P.N. Hoffman, J.F. Humphreys, Projective representations of the symmetric group, Oxford Mathematical Monographs, Clarendon Press Oxford, (1992).
I.M. Isaacs, Character theory of finite groups, Academic Press (1976).
G.D. James, A. Kerber, The representations of the symmetric group, Encyclope-dia of Mathematics and its Applications 16, Addison-Wesley (1981).
H.I. Jones, Clifford algebras and representations of generalised symmetric gro-upsPh.D. thesis, University of Wales, Aberystwyth (1993).
A. Kerber, Zur modularen Darstellungstheorie symmetrischer und alternierender Gruppen, Mitt. Math. Sem. Univ. Giessen 68 (1966), 1–80.
A. Kerber, Zur Darstellungstheorie von Kranzprodukten, Canad. J. Math. 20 (1968), 665–672.
A. Kerber, Representations of permutation groups, I and II, Lecture Notes in Mathematics 240 (1971), 495 (1975) Springer-Verlag, Berlin.
A. Lascoux, B. Leclerc, J-Y. Thibon, Ribbon tableaux, Hall-Littlewood functions, quantum affine algebras and unipotent elements, J. Math. Physics 38 (1997), 1041–1068.
R.J. List, I.M.I. Mahmoud, Fischer matrices for wreath products G I Sn, Arch. Math. 50 (1988), 394–401.
16.M. Osima, On the representations of the generalized symmetric group, Math. J. Okayama Univ. 4 (1954), 39–56; II, (ibid) 6 (1956), 81–97.
17.E.W. Read, The a-regular classes of the generalized symmetrized group, Glasgow Math. J. 17 (1976), 144–s150.
E.W. Read, The projective representations of the generalized symmetric group, J. Algebra 46 (1977), 102–132. Combinatorics of Characters of Group Extensions 293
I. Schur, Űber die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Subsitutionen, J. Reine Ang. Math. 139 1911, 155–250.
W.Specht, Eine Verallgemeinerung der symmetrischen Gruppe. Schriften des Math. Sem. Berlin 1 (1932), 1–32.
W. Specht, Eine Verallgemeinerung der Permutationsgruppe, Math. Zeits. 37 (1933), 321–341.
W. Specht, Darstellungstheorie der Hyperoktaedergruppe, Math. Zeits. 42 (1937), 629–640.
R.P. Stanley, Enumerative Combinatorics, Vol. I, Wadsworth Books, Monterey, California (1986).
J.R. Stembridge, The projective representations of the hyperoctahedral group, J. Algebra 145 (1992), 396–453.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Morris, A., Almestady, M. (2001). The Combinatorics of the Character Theory for some Group Extensions. In: Betten, A., Kohnert, A., Laue, R., Wassermann, A. (eds) Algebraic Combinatorics and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59448-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-59448-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41110-9
Online ISBN: 978-3-642-59448-9
eBook Packages: Springer Book Archive