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On Certain Stable Wedge Summands of B(đ“©/p)n+

Published online by Cambridge University Press:  20 November 2018

John C. Harris
John C. Harris*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1 (harris@math.toronto.edu)
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Abstract

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Campbell and Selick have given a natural decomposition of the cohomology of an elementary abelian p-group over the Steenrod algebra. We study the corresponding stable wedge summands of the classifying space B(đ“©/p)n+ using representation theory and explicit idempotents in the group ring 𝓕p[GLn(đ“©/p)].

Keywords

55P4255S10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 104 - 118
Copyright
Copyright © Canadian Mathematical Society 1989

References

[AGM] Adams, J.F., Gunawardena, J.H., and Miller, H.R., The Segal conjecture for elementary abelian pgroups, Topology 24(1985), 435–460.Google Scholar
[A] AguadĂ©, J., The cohomologyojGL2 of a finite field, Arch. Math. 34(1980), 509–516.Google Scholar
[CS] A, H.E.. Campbell and Selick, R. S., Polynomial algebras over the Steenrod algebra, Comment. Math. Helv., 65(1990) 171–180.Google Scholar
[C] Carlisle, D., The modular representation theory ofGL(n,p), and applications to topology. Ph.D. thesis, University of Manchester, 1985.Google Scholar
[CK] Carlisle, D.and Kuhn, N.J., Subalgebras of the Steenrod algebra and the action of matrices on truncated polynomial algebras, J. Algebra 121(1989), 370–387.Google Scholar
[CW] Carlisle, D.P. and Walker, G., Poincaré series for the occurrence of certain modular representations of GL(n,p) in the symmetric algebra, preprint (1989).Google Scholar
[Ca] Carlsson, G., Equivariant stable homotopy and Segals Burnside ring conjecture, Ann. of Math. (2) 120(1984), 189–224.Google Scholar
[Co] Cohen, F., Splitting certain suspensions via self-maps, 111. J. Math. 20(1976), 336–347.Google Scholar
[CRI] Curtis, C.W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras. Wiley, 1962.Google Scholar
[CR2] Curtis, C.W., Methods of Representation Theory, vol. 1, Wiley, 1981.Google Scholar
[D] Davenport, H., Bases for finite fields, J. London Math. Soc. 43(1968), 21–39.Google Scholar
[H] Harris, J.C., Stable splittings of classifying spaces. Ph.D. thesis, University of Chicago, 1985.Google Scholar
[HK] Harris, J.C. and Kuhn, N.J., Stable decompositions of classifying spaces of finite abelian p-groups, Math. Proc. Camb. Phil. Soc. 103(1988), 427^49.Google Scholar
[HB] Huppertand, B., Blackburn, N., Finite Groups, II. Springer-Verlag, 1982.Google Scholar
[JK] James, G.and Kerber, A., The Representation Theory of the Symmetric group. Encyclopedia of Math, and its Applications, 16, Addison-Wesley, 1981.Google Scholar
[K] Kuhn, N.J., The Morava K-theory of some classifying spaces, Trans. Amer. Math. Soc. 304(1987), 193–205.Google Scholar
[LS] Lannes, J.and Schwartz, L., Sur la structure des A-modules instable injectifs, Topology 28(1989), 153–169.Google Scholar
[LZ1] Lannes, J.and Zarati, S., Sur les 풰 -injectives, Ann. Scient. Ec. Norm. Sup. 19(1986), 303–333.Google Scholar
[LZ2] Lannes, J.and Zarati, S.,Sur les fondeurs dĂ©rivĂ©s de la dĂ©stabilisation, Math. Z. 194(1987), 25–59.Google Scholar
[M] May, J.P., Stable maps between classifying spaces, Amer. Math. Soc. Cont. Math. 37(1985), 121–129.Google Scholar
[Mi] Miller, H.R., The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120(1984), 39–87.Google Scholar
[Mil] Mitchell, S.A., Splitting B(Z/p)n andBTn via modular representation theory, Math. Z. 189(1985), 1–9.Google Scholar
[Mi2] Mitchell, S.A., Finite complexes with A(n)-free cohomology, Topology 24(1985), 227–248.Google Scholar
[MP] Mitchell, S.A. and Priddy, S.B., Stable splittings derived from the Steinberg module, Topology 22(1983), 285–298.Google Scholar
[N] Nishida, G., Stable homotopytype of classifying spaces of finite groups, Algebraic and Topological Theories (1985),391–404.Google Scholar
[S] Stanley, R.P., Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (1) 3(1979), 475–511.Google Scholar
[T] Tucker, P.A., On the reduction of induced representations of finite groups, Amer. J. Math. 84(1962), 400–420.Google Scholar
[W] Witten, C.M., Self-maps of classifying spaces of finite groups and classification of low-dimensional Poincaré duality spaces. Ph.D. Thesis, Stanford University, 1978.Google Scholar
[Wo] W, R.M. Wood, Splitting Z(CP∞ x ̇ ̇ ̇ x CP∞) and the action of Steenrodsquares Sql on the polynomial ring F2[jq,
 ,xn], in Algebraic Topology Barcelona 1986, Lecture Notes in Math. 1298 Springer 1987, 237–255.Google Scholar