On the correspondence of representations between 𝐺𝐿(𝑛) and division algebras

Lansky, Joshua; Raghuram, A.

doi:10.1090/S0002-9939-02-06918-6

On the correspondence of representations between $GL(n)$ and division algebras
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by Joshua Lansky and A. Raghuram PDF

Proc. Amer. Math. Soc. 131 (2003), 1641-1648 Request permission

Abstract:

For a division algebra $D$ over a $p$-adic field $F,$ we prove that depth is preserved under the correspondence of discrete series representations of $GL_n(F)$ and irreducible representations of $D^*$ by proving that an explicit relation holds between depth and conductor for all such representations. We also show that this relation holds for many (possibly all) discrete series representations of $GL_2(D).$

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