Taiwanese Journal of Mathematics

SIMPLE SUPERCUSPIDAL REPRESENTATIONS OF $\operatorname{GL}(n)$

Andrew Knightly and Charles Li

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Abstract

Following a construction of Gross and Reeder, we define simple supercuspidal  representations of $\operatorname{GL}(n)$ over a $\mathfrak{p}$-adic field.  We show that they have conductor $\mathfrak{p}^{n+1}$.  We then give a general formula for  the matrix coefficient attached to a new vector, and make it  completely explicit when $n=2$.

Article information

Source
Taiwanese J. Math., Volume 19, Number 4 (2015), 995-1029.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133686

Digital Object Identifier
doi:10.11650/tjm.19.2015.3853

Mathematical Reviews number (MathSciNet)
MR3384676

Zentralblatt MATH identifier
1357.22009

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Keywords
simple supercuspidal representation matrix coefficient new vector

Citation

Knightly, Andrew; Li, Charles. SIMPLE SUPERCUSPIDAL REPRESENTATIONS OF $\operatorname{GL}(n)$. Taiwanese J. Math. 19 (2015), no. 4, 995--1029. doi:10.11650/tjm.19.2015.3853. https://projecteuclid.org/euclid.twjm/1499133686


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