The alternating sum of parabolic inductions and restrictions of an affine Hecke algebra module equals a module twisted by an explicit sign-and-parameter involution, with a finite-group analogue proved under restrictive assumptions.
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An involution for Hecke algebras
The alternating sum of parabolic inductions and restrictions of an affine Hecke algebra module equals a module twisted by an explicit sign-and-parameter involution, with a finite-group analogue proved under restrictive assumptions.