Regular characters of $GL_n(O)$ and Weil representations over finite fields

@article{Takase2015RegularCO,
  title={Regular characters of \$GL\_n(O)\$ and Weil representations over finite fields},
  author={Koichi Y. Takase},
  journal={arXiv: Representation Theory},
  year={2015}
}
  • K. Takase
  • Published 15 October 2015
  • Mathematics
  • arXiv: Representation Theory
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References

SHOWING 1-10 OF 13 REFERENCES
On the nilpotent representations ofGLn(O)
In a previous paper, we produced a “Jordan decomposition of characters” for the groupsGLn(O), whereO is the ring of integers in ap-adic field, splitting the representation theory into “nilpotent” and
On some explicit formulas in the theory of Weil representation
The object of this paper is to derive some explicit formulae concerning the Weil representation that allow us to define this projective representation in a unique manner for each choice of symplectic
The characters of the finite general linear groups
Introduction. In this paper we show how to calculate the irreducible characters of the group GL(n, q) of all nonsingular matrices of degree n with coefficients in the finite field of q elements.
The Smooth Representations of GL2(𝔒)
We give a classification of the smooth (complex) representations of GL2(𝔬), where 𝔬 is the ring of integers in a non-Archimedean local field. The approach is based on Clifford theory of finite
Gauss Sums and p-adic Division Algebras
Arithmetic of local division algebras.- to Gauss Sums.- Functional equation.- One-dimensional representations.- The basic correspondence.- The basic inductive step.- The general inductive process.-
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