Grading the Translation Functors in type A

2003/01/24 by Steen Ryom-Hansen, Ryom-Hansen, Steen
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0301285

openalex publication_date 2003/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with the representation theory of quantum groups and Hecke algebras at roots of unity. We relate the philosophy of Andersen, Jantzen and Soergel on graded translated functors to the Lascoux, Leclerc and Thibon-algorithm. This goes via the Murphy standard basis theory and the idempotents coming from the Murphy-Jucys operators. Our results lead to a guess on a tilting algorithm outside the lowest p² alcove, which at least in the SL₂-case coincides with Erdmann's results.

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