Geodesic
Projective and Multigraded Representations of Monomial and Multisigned Groups I. Graded Representations of a Twisted Product
Canadian journal of mathematics, Tome 45 (1993) no. 2, pp. 295-339

Voir la notice de l'article provenant de la source Cambridge University Press

Motivated by the problem of giving a functorial (or at least uniform) description of the projective representations for wreath products Gʅ Sn in terms of thosefor G, we study a certain binary operation on the class of “cyclic covering groups with parities”. Along with setting up the basic machinery associated to representations graded by (Ζ/2)l , the main result is a description of the irreducibles for in terms of a (tensorlike) product of those for Aand for B.Finally we describe a programme for producing a PSH-algebra theory in this context, analogous to that of Zelevinsky for the case l=0, and that of the author withwith Michael Bean (structure) and with John Humphreys (applications) for the case l=1
DOI : 10.4153/CJM-1993-015-8
Mots-clés : 20C25, 20C15, 16A24, 20C30 
Hoffman, Peter. Projective and Multigraded Representations of Monomial and Multisigned Groups I. Graded Representations of a Twisted Product. Canadian journal of mathematics, Tome 45 (1993) no. 2, pp. 295-339. doi: 10.4153/CJM-1993-015-8
@article{10_4153_CJM_1993_015_8,
     author = {Hoffman, Peter},
     title = {Projective and {Multigraded} {Representations} of {Monomial} and {Multisigned} {Groups} {I.} {Graded} {Representations} of a {Twisted} {Product}},
     journal = {Canadian journal of mathematics},
     pages = {295--339},
     year = {1993},
     volume = {45},
     number = {2},
     doi = {10.4153/CJM-1993-015-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-015-8/}
}
TY  - JOUR
AU  - Hoffman, Peter
TI  - Projective and Multigraded Representations of Monomial and Multisigned Groups I. Graded Representations of a Twisted Product
JO  - Canadian journal of mathematics
PY  - 1993
SP  - 295
EP  - 339
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-015-8/
DO  - 10.4153/CJM-1993-015-8
ID  - 10_4153_CJM_1993_015_8
ER  - 
%0 Journal Article
%A Hoffman, Peter
%T Projective and Multigraded Representations of Monomial and Multisigned Groups I. Graded Representations of a Twisted Product
%J Canadian journal of mathematics
%D 1993
%P 295-339
%V 45
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-015-8/
%R 10.4153/CJM-1993-015-8
%F 10_4153_CJM_1993_015_8

[A-B-S] Atiyah, M.F., Bott, R. and Shapiro, A., Clifford modules, Topology (1) 3(1964), 3–38. Google Scholar

[A-T] Atiyah, M.F. and Tall, D.O., Group representations,ƛ-rings, and the J-homomorphism, Topology 8(1969), 253–297. Google Scholar

[B] Bean, M., Unpublished manuscript, 1988. Google Scholar

[B-H] Bean, M. and Hoffman, P.N., Zelevinsky algebras related to projective representations, Trans. Amer. Math. Soc. 309(1988), 99–111. Google Scholar

[D] Dade, E.C., Compounding Clifford's theory, Ann. Math. (2) 91(1970), 236–290. Google Scholar

[H-Hl] Hoffman, P.N. and Humphreys, J.F., Hopf algebras and projective representations ofG\Sn and GlAn, Can. J. Math. 38(1986), 1380–1458. Google Scholar

[H-H2] Hoffman, P.N., Projective representations of generalized symmetric groups using PSH-algebras, Proc. London Math. Soc. (3) 59(1989), 483–506. Google Scholar

[H-H3] Hoffman, P.N., Projective Representations of the Symmetric Groups, Oxford University Press, Oxford, 1992. Google Scholar

[Md] Macdonald, I.G., Symmetric Functions and Hall Polynomials, Oxford University Press, Oxford, 1979. Google Scholar

[Ml] MacLane, S., Homology, Springer-Verlag, New York, 1967. Google Scholar

[Rl] Read, E.W., On the projective characters of the symmetric group, J. London Math. Soc. (2) 15(1977), 456–464. Google Scholar

[R2] Read, E.W., On the Schur multiplier of a wreath product, Illinois J. Math. 20(1976), 456–466. Google Scholar

[S] Schmid, P., Clifford theory of simple modules, Proc. of Symposia in Pure Math. AMS (2) 47(1987), 75–82. Google Scholar

[Z] Zelevinsky, A.V., Representations of Finite Classical Groups—a Hopf Algebra Approach, Lecture Notes in Mathematics 869, Springer-Verlag, Berlin, 1981. Google Scholar

Cité par Sources :