比利时vs摩洛哥足彩
,
university of california san diego
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representation theory
peter trapa
university of utah
unipotent representations and the theta correspondence.
abstract:
fix a real reductive group $g$. suppose $mathcal{o}'$ is a nilpotent orbit in $mathfrak{g}'$, the dual of the complexified lie algebra of $g$. to each $x' in mathcal{o}'$, one may associate an sl(2) triple, say $x', y'$, and $h'$. since $(1/2)h'$ lives in a cartan subalgebra of $mathfrak{g}'$, it defines an infinitesimal character for $g$. one piece of the arthur conjectures predicts that the smallest representations of $g$ with infinitesimal character $(1/2)h'$ should appear as local components of automorphic forms; in particular, they should be unitary. (two good examples to keep in mind are the trivial representation and limits of discrete series with zero infinitesimal character; the former corresponds to the principal orbit $mathcal{o'}$ and the latter to the zero orbit.) in this talk, we explain how to prove a large part of this conjecture for certain classical groups using the theta correspondence.
host: wee teck gan
february 24, 2004
1:30 pm
ap&m 7321
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