## 6 Citations

Representations of $\mathrm{GL}_N$ over finite local principal ideal rings - an overview

- Mathematics
- 2017

We give a survey of the representation theory of $\mathrm{GL}_N$ over finite local principal ideal rings via Clifford theory, with an emphasis on the construction of regular representations. We…

Regular irreducible represntations of classical reductive groups over finite quotient rings

- Mathematics
- 2019

A parametrization of irreducible representations associated with a regular adjoint orbit of a reductive group over finite quotient rings of a non-dyadic non-archimedean local filed is presented. The…

A multiplicity one theorem for groups of type $A_n$ over discrete valuation rings

- Mathematics
- 2018

Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field with the maximal ideal $\wp$ and the finite residue field of characteristic $p.$ Let $\mathbf{G}$ be the General Linear or…

Regular characters of classical groups over complete discrete valuation rings

- MathematicsJournal of Pure and Applied Algebra
- 2019

Regular irreducible representations of classical groups over finite quotient rings

- Mathematics
- 2019

A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local…

## References

SHOWING 1-10 OF 13 REFERENCES

On the nilpotent representations ofGLn(O)

- Mathematics
- 1994

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

- Mathematics
- 1993

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

- Mathematics
- 1955

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)

- Mathematics
- 2008

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

- Mathematics
- 1983

Arithmetic of local division algebras.- to Gauss Sums.- Functional equation.- One-dimensional representations.- The basic correspondence.- The basic inductive step.- The general inductive process.-…