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Peer-reviewedCC BY 4.0Algebraic Combinatorics

Hecke combinatorics, Kåhrström’s conditions and Kostant’s problem

  • Samuel Creedon1
  • Volodymyr Mazorchuk1
  1. 1Department of Mathematics, Uppsala University, Box. 480, SE-75106, Uppsala, Sweden
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Abstract

This paper discusses various aspects of the Hecke algebra combinatorics that are related to conditions appearing in Kåhrström’s conjecture, which addresses Kostant’s problem for simple highest weight modules in the Bernstein-Gelfand-Gelfand category 𝒪 for the complex Lie algebra 𝔰𝔩 n . In particular, we study cyclic submodules of the regular Hecke module that are generated by the elements of the (dual) Kazhdan–Lusztig basis as well as the problem of left cell invariance for both categorical and combinatorial Kåhrström’s conditions.

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Cite

BibTeXRIS
BibTeX
@article{creedon2026hecke,
  title = {{Hecke combinatorics, Kåhrström’s conditions and Kostant’s problem}},
  author = {Samuel Creedon and Volodymyr Mazorchuk},
  journal = {Algebraic Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.5802/alco.510},
  url = {https://alco.centre-mersenne.org/articles/10.5802/alco.510/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Hecke combinatorics, Kåhrström’s conditions and Kostant’s problem
AU  - Samuel Creedon
AU  - Volodymyr Mazorchuk
PY  - 2026
DA  - 2026/10/27
JO  - Algebraic Combinatorics
DO  - 10.5802/alco.510
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.510/
AB  - This paper discusses various aspects of the Hecke algebra combinatorics that are related to conditions appearing in Kåhrström’s conjecture, which addresses Kostant’s problem for simple highest weight modules in the Bernstein-Gelfand-Gelfand category 𝒪 for the complex Lie algebra 𝔰𝔩 n . In particular, we study cyclic submodules of the regular Hecke module that are generated by the elements of the (dual) Kazhdan–Lusztig basis as well as the problem of left cell invariance for both categorical and combinatorial Kåhrström’s conditions.
SN  - 2589-5486
ER  -