Abstract
We show that between any pair of Galois conjugate blocks of a finite group, there is an isotypy with all signs positive.
2000 Mathematics Subject Classification: MSC 2000: 20C99
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
J. Alperin and M. Broué, Local methods in block theory, Ann. of Math 110 (1979), 143–157
D. J. Benson and R. Kessar, Blocks inequivalent to their Frobenius twists, J. Algebra 315 (2007), no. 2, 588–599
R. Boltje, B. Xu, On p-permutation equivalences: between Rickard equivalences and isotypies. Trans. Amer. Math. Soc. 360 (2008), no. 10, 5067–5087
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), 361–365
M. Broué, Blocs, Isométries parfaites, catégories dériveés C.R. Acd. Sci. Paris 307, Serie I (1988), 13–18
M. Broué, Isométries parfaites, types de blocs, catégories dériveés, Astérisque 181–182 (1990), 61–91
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, 1987
P. Fong and M. Harris, On perfect isometries and isotypies in finite groups, Invent. Math. 114 (1993), no.1, 139–191
R. Kessar, A remark on Donovan’s conjecture, Arch. Math (Basel) 82 (2004), 391–394
M. Linckelmann, Trivial Source bimodule rings for blocks and p-permutation equivalences Trans. Amer. Math. Soc. 361 (2009), 3, 1279–1316
H. Nagao, Y. Tsushima, Representations of finite groups, Academic Press, 1988
J. P. Serre, Corps locaux, Hermann, 1968
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this paper
Cite this paper
Kessar, R. (2012). On Isotypies Between Galois Conjugate Blocks. In: Sastry, N. (eds) Buildings, Finite Geometries and Groups. Springer Proceedings in Mathematics, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0709-6_7
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0709-6_7
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0708-9
Online ISBN: 978-1-4614-0709-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)