PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{ciubotaru2026jantzen,
title = {{Jantzen filtrations for graded affine Hecke algebras}},
author = {Dan Ciubotaru},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03651},
eprint = {2609.03651},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03651},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Jantzen filtrations for graded affine Hecke algebras
AU - Dan Ciubotaru
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.03651
UR - https://arxiv.org/abs/2609.03651
AB - 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.
ER -