Abstract
In finite group modular representation theory, the Green correspondence for indecomposable modules is a fundamental correspondence. Also, subpairs (of J.L. Alperin and M. Broué) comprise a basic structure in this theory. The Harris-Knörr correspondence for blocks is a Clifford theoretic extension of R. Brauer’s first main theorem on blocks and using a basic idea of the Harris-Knörr results and the Green correspondence, J.L. Alperin proved a corresponding correspondence for indecomposable modules. In this paper, we reduce the hypotheses of each of those three correspondences to hypotheses on the normalizers of appropriate subpairs.
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References
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Harris, M.E. Morita equivalences and basic correspondences. Arch. Math. 119, 27–35 (2022). https://doi.org/10.1007/s00013-022-01707-3
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DOI: https://doi.org/10.1007/s00013-022-01707-3