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On Isotypies Between Galois Conjugate Blocks

  • Radha KessarEmail author
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 10)

Abstract

We show that between any pair of Galois conjugate blocks of a finite group, there is an isotypy with all signs positive.

Galois conjugate blocks Centers Isotypy 

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References

  1. 1.
    J. Alperin and M. Broué, Local methods in block theory, Ann. of Math 110 (1979), 143–157Google Scholar
  2. 2.
    D. J. Benson and R. Kessar, Blocks inequivalent to their Frobenius twists, J. Algebra 315 (2007), no. 2, 588–599Google Scholar
  3. 3.
    R. Boltje, B. Xu, On p-permutation equivalences: between Rickard equivalences and isotypies. Trans. Amer. Math. Soc. 360 (2008), no. 10, 5067–5087Google Scholar
  4. 4.
    R. Brauer, W. Feit, On the number of irreducible characters of finite groups in a given block Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 361–365Google Scholar
  5. 5.
    M. Broué, Blocs, Isométries parfaites, catégories dériveés C.R. Acd. Sci. Paris 307, Serie I (1988), 13–18Google Scholar
  6. 6.
    M. Broué, Isométries parfaites, types de blocs, catégories dériveés, Astérisque 181–182 (1990), 61–91Google Scholar
  7. 7.
    G. Cliff, W. Plesken. A. Weiss, Order-theoretic properties of the center of a block. The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), 413–420, Proc. Sympos. Pure Math., 47, Part 1, Amer. Math. Soc., Providence, RI, 1987Google Scholar
  8. 8.
    P. Fong and M. Harris, On perfect isometries and isotypies in finite groups, Invent. Math. 114 (1993), no.1, 139–191Google Scholar
  9. 9.
    R. Kessar, A remark on Donovan’s conjecture, Arch. Math (Basel) 82 (2004), 391–394Google Scholar
  10. 10.
    M. Linckelmann, Trivial Source bimodule rings for blocks and p-permutation equivalences Trans. Amer. Math. Soc. 361 (2009), 3, 1279–1316Google Scholar
  11. 11.
    H. Nagao, Y. Tsushima, Representations of finite groups, Academic Press, 1988Google Scholar
  12. 12.
    J. P. Serre, Corps locaux, Hermann, 1968Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute of Mathematics, Fraser Noble Building, King’s CollegeUniversity of AberdeenAberdeenUK

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