# On generic supercuspidal representations of $Sp_{2n}$

## TL;DR

This paper constructs a broad family of irreducible generic supercuspidal representations for symplectic groups over non-archimedean local fields, using compact induction from finite symplectic group representations.

## Contribution

It introduces a new method to explicitly construct supercuspidal representations of symplectic groups via compact induction from finite symplectic groups.

## Key findings

- Explicit construction of supercuspidal representations
- Use of compact induction from finite symplectic groups
- Representation inflation from finite quotient rings

## Abstract

We will construct a family of irreducible generic supercuspidal representations of the symplectic groups over non-archimedian local field $F$ of odd residual characteristic. The supercuspidal representations are compactly induced from irreducible representations of the hyperspecial compact subgroup which are inflated from irreducible representations of finite symplectic groups over the finite quotient ring of the integer ring of $F$ modulo high powers of the prime element.