Jantzen filtrations for graded affine Hecke algebras

Abstract

We prove the Jantzen conjecture for standard modules of graded affine Hecke algebras with equal parameters, real central character in the dominant deformation direction. The Jantzen layers are shown to be semisimple, and the multiplicities are given by the full local intersection cohomology of the corresponding orbit closures. The proof identifies the algebraic standard-to-contragredient map with the costalk-to-stalk map on a contracting transverse slice. Hard Lefschetz theorem determines its elementary divisors, and a residual grading on the specialized convolution algebra proves semisimplicity. An example in type $A$ is included to show that dominance is necessary.

arXiv comment48 pages, use of AI