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locally analytic

Journal of the Institute of Mathematics of Jussieu (1)

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LOCALLY ANALYTIC CUSPIDAL REPRESENTATIONS FOR $\mathrm{GL}_2$ AND RELATED GROUPS
Mark Kisin, Matthias Strauch
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 5 / Issue 3 / July 2006

Published online by Cambridge University Press:

15 February 2006, pp. 373-421

Print publication:

July 2006
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For a finite extension $F/\mathbb{Q}_p$ we construct and study a class of locally analytic representations of GL$_2(F)$ and related groups such as the quaternion algebra over $F$. The construction is based on inducing a locally analytic character of a maximal torus. We show that for a generic character the resulting representation is topologically irreducible, and not isomorphic to a locally analytic principal series, when the torus is non-split.