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PreprintarXiv licencearXiv

Unequal-parameter Kostka--Foulkes polynomials of type Cn at fundamental weights

  • Murilo Corato-Zanarella
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Abstract

We establish an explicit formula for the Kostka--Foulkes polynomial of type Cn with unequal parameters at fundamental weights. As an application, we deduce an explicit Lusztig--Kato formula for the Hecke algebra of the special (but not hyperspecial) maximal compact subgroup of a quasi-split but non-split special orthogonal group over a p-adic field.

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Cite

BibTeXRIS
BibTeX
@misc{coratozanarella2026unequalparameter,
  title = {{Unequal-parameter Kostka--Foulkes polynomials of type $C_n$ at fundamental weights}},
  author = {Murilo Corato-Zanarella},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39095},
  eprint = {2609.39095},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39095},
}
RIS
TY  - UNPB
TI  - Unequal-parameter Kostka--Foulkes polynomials of type C_n at fundamental weights
AU  - Murilo Corato-Zanarella
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39095
UR  - https://arxiv.org/abs/2609.39095
AB  - We establish an explicit formula for the Kostka--Foulkes polynomial of type C_n with unequal parameters at fundamental weights. As an application, we deduce an explicit Lusztig--Kato formula for the Hecke algebra of the special (but not hyperspecial) maximal compact subgroup of a quasi-split but non-split special orthogonal group over a p-adic field.
ER  -