WorkshopsLocally analytic vectors of unitary principal series of GL<sub>2</sub>(<strong>Q</strong><sub><i>p</i></sub>)
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The p-adic local Langlands correspondence for GL2(Qp), which is initiated by Breuil and established by Colmez, attaches an admissible unitary representation Π(V) of GL2(Qp) to any 2-dimensional irreducible representation V of GQp. The unitary principal series of GL2(Qp) are those admissible unitary representations corresponding to trianguline representations. Although the present version of the p-adic local Langlands correspondence for GL2(Qp) is formulated at the level of admissible unitary representations, it is very useful, as in Breuil's original works (and many other examples), to have the information of the space of locally analytic vectors Π(V)an of Π(V). The main result of this talk is a determination of the space of locally analytic vectors for all (non-exceptional) unitary principle series of GL2(Qp); this proves a conjecture of Emerton. This is a joint work with Bingyong Xie and Yuancao Zhang.
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Ruochuan Liu
2010-07-14
15:40:00 - 17:00:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
The p-adic local Langlands correspondence for GL2(Qp), which is initiated by Breuil and established by Colmez, attaches an admissible unitary representation Π(V) of GL2(Qp) to any 2-dimensional irreducible representation V of GQp. The unitary principal series of GL2(Qp) are those admissible unitary representations corresponding to trianguline representations. Although the present version of the p-adic local Langlands correspondence for GL2(Qp) is formulated at the level of admissible unitary representations, it is very useful, as in Breuil's original works (and many other examples), to have the information of the space of locally analytic vectors Π(V)an of Π(V). The main result of this talk is a determination of the space of locally analytic vectors for all (non-exceptional) unitary principle series of GL2(Qp); this proves a conjecture of Emerton. This is a joint work with Bingyong Xie and Yuancao Zhang.