Alvis–Curtis duality

In mathematics, the Alvis–Curtis duality is a duality operation on the characters of a reductive group over a finite field, introduced by Charles W. Curtis (1980) and studied by his student Dean Alvis (1979). Kawanaka (1981, 1982) introduced a similar duality operation for Lie algebras.

Alvis–Curtis duality has order 2 and is an isometry on generalized characters.

Carter (1985, 8.2) discusses Alvis–Curtis duality in detail.

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