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Peer-reviewedCC BY 4.0Proceedings of the London Mathematical Society

Completed Iwahori–Hecke algebra for Kac–Moody groups over local fields

  • Auguste Hébert
  • Dinakar Muthiah
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Abstract

Let G be a split Kac–Moody group over a non‐Archimedean local field, and ℋ let be the Iwahori–Hecke algebra of . In this paper, we construct a completed Iwahori–Hecke algebra and prove that it contains a large center isomorphic to Looijenga's invariant ring. By the Kac–Moody Satake isomorphism, Looijenga's invariant ring is isomorphic to the spherical Hecke algebra. We prove that our completion is equal to Iwahori biinvariant functions on satisfying a support condition that we call Weyl almost finite support .

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Cite

BibTeXRIS
BibTeX
@article{hebert2026completed,
  title = {{Completed Iwahori–Hecke algebra for Kac–Moody groups over local fields}},
  author = {Auguste Hébert and Dinakar Muthiah},
  journal = {Proceedings of the London Mathematical Society},
  year = {2026},
  month = aug,
  doi = {10.1112/plms.70189},
  eprint = {2510.17559},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05743118v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Completed Iwahori–Hecke algebra for Kac–Moody groups over local fields
AU  - Auguste Hébert
AU  - Dinakar Muthiah
PY  - 2026
DA  - 2026/08/22
JO  - Proceedings of the London Mathematical Society
DO  - 10.1112/plms.70189
UR  - https://hal.science/hal-05743118v1
AB  - Let G be a split Kac–Moody group over a non‐Archimedean local field, and ℋ let be the Iwahori–Hecke algebra of . In this paper, we construct a completed Iwahori–Hecke algebra and prove that it contains a large center isomorphic to Looijenga's invariant ring. By the Kac–Moody Satake isomorphism, Looijenga's invariant ring is isomorphic to the spherical Hecke algebra. We prove that our completion is equal to Iwahori biinvariant functions on satisfying a support condition that we call Weyl almost finite support .
SN  - 0024-6115
SN  - 1460-244X
ER  -