Abstract
When Richard Brauer, facing the difficulty of determining the irreducible modular characters of a block b, introduced in [1] the notion of basic set, was he aware that the invariant behind the corresponding generalized decomposition matrices is just the center of b, endowed with the ideal generated by the ordinary characters? Here, we will not try to answer this question but only to provide a proof of this fact, which, as far as we know, has never been published.
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References
R. Brauer, Some applications of the theory of blocks of characters of finite groups I, J. of Alg. 1 (1964), 152–167.
R. Brauer, Types of blocks of representations of finite groups, Proc. Symp. Pure Math. 21 (1971), 7–11.
M. Broué, Radical, hauteurs, p-sections et blocs, Ann. of Math. 107 (1978), 89–107.
L. Puig, Sur un théorème de Green, Math. Z. 166 (1979), 117–129.
L. Puig, Pointed groups and construction of characters, Math. Z. 176 (1981), 265–292.
L. Puig, Y. Usami, Perfect isometries for blocks with abelian defect groups and Klein four inertia! quotients, J. of Alg. 160 (1993), 192–225.
W. Reynolds, Sections and ideals of centers of group elements, J. of Alg. 20 (1972) 176–181.
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© 1997 Birkhäuser Boston
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Puig, L. (1997). The Center of a Block. In: Cabanes, M. (eds) Finite Reductive Groups: Related Structures and Representations. Progress in Mathematics, vol 141. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4124-9_14
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DOI: https://doi.org/10.1007/978-1-4612-4124-9_14
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8664-6
Online ISBN: 978-1-4612-4124-9
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