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PreprintCC BY 4.0arXiv

The Extension groups of one K-type representations of graded Hecke algebra

  • Quanyong Chen
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Abstract

We study the extension groups between one K-type representations of the graded Hecke algebra ℍ. A one K-type representation is a Hermitian representation of mbb H whose restriction to the Weyl group is irreducible. Using a Koszul-type resolution of ℍ-modules, we reduce the computation of Extℍj(X,Y) to a combinatorial count, yielding explicit formulas for the classical types and a computer computation for the exceptional types.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026extension,
  title = {{The Extension groups of one $\rm K$-type representations of graded Hecke algebra}},
  author = {Quanyong Chen},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04535},
  eprint = {2611.04535},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04535},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Extension groups of one K-type representations of graded Hecke algebra
AU  - Quanyong Chen
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04535
UR  - https://arxiv.org/abs/2611.04535
AB  - We study the extension groups between one K-type representations of the graded Hecke algebra ℍ. A one K-type representation is a Hermitian representation of mbb H whose restriction to the Weyl group is irreducible. Using a Koszul-type resolution of ℍ-modules, we reduce the computation of Ext_ℍ^j(X,Y) to a combinatorial count, yielding explicit formulas for the classical types and a computer computation for the exceptional types.
ER  -