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Unitarity, Eisenstein series, Arthur's conjectures, and intertwining operators (Unitary Dual Workshop)
Stephen D. Miller, Rutgers
Location: Hill 705
Date & time: Wednesday, 29 January 2020 at 3:30PM - 4:30PM
Inspired by the trace formula, Jim Arthur has conjectured the existence of some exotic "unipotent" representations of real reductive Lie groups, which in some sense are expected to form building blocks of the unitary dual. Though falling short of a full classification of the unitary dual itself, these conjectures touch on the essense of some of the most difficult questions concerning unitarity.
Arthur's unipotent representations are hard to identify, much less even prove the desired unitary of. I'll present a status report, including the unitary of the "Langlands element" Arthur describes directly. Time permitting, I'll also discuss some methods developed by Zhuohui Zhang in his Rutgers Ph.D. thesis for computing intertwining operators Hermitian forms on K-types.