Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Ciubotaru, Dan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208714335