Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unicity of types for supercuspidal representations of p-adic SL(2)   We consider the question of unicity of types on maximal compact subgroups for
supercuspidal representations of $\mathbf{SL}_2$ over a nonarchimedean local
field of odd residual characteristic. We introduce the notion of an archetype
as the $\mathbf{SL}_2$-conjugacy class of a typical representation of a maximal
compact subgroup, and go on to show that any archetype in $\mathbf{SL}_2$ is
restricted from one in $\mathbf{GL}_2$. From this it follows that any archetype
must be induced from a Bushnell--Kutzko type. Given a supercuspidal
representation $\pi$, we give an additional explicit description of the number
of archetypes admitted by $\pi$ in terms of its ramification. We also describe
a relationship between archetypes for $\mathbf{GL}_2$ and $\mathbf{SL}_2$ in
terms of $L$-packets, and deduce an inertial Langlands correspondence for
$\mathbf{SL}_2$.

12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: stat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
1
The categories of this paper are: cs