The most fundamental unsolved problem in the representation theory of Lie groups is the Problem of the Unitary Dual: given a reductive Lie group G, this problem asks for a parameterization of the set of irreducible unitary G-representations. There are two big "philosophies" for approaching this problem. The Orbit Method of Kostant and Kirillov seeks to parameterize irreducible unitary representations in terms of finite covers of co-adjoint G-orbits. Arthur's conjectures suggest a parameterization in terms of certain combinatorial gadgets (i.e. Arthur parameters) related to the Langlands dual group G^{\vee} of G. In this talk, I will define these correspondences precisely in the case of complex groups. I will also define a natural duality map from Arthur parameters (for G^{\vee}) to co-adjoint covers (for G) which, in a certain precise sense, intertwines these correspondences. This talk is partially based on joint work with Ivan Losev and Dmitryo Matvieievskyi.
De Pierre-Henri Chaudouard
De Pierre-Henri Chaudouard
De Lucas Mason-Brown
De Xinwen Zhu
De Xinwen Zhu
De Xinwen Zhu
De Tasho Kaletha
De Bao Chau Ngo
De Bao Chau Ngo
De Tasho Kaletha
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Bao Chau Ngo
De Sam Raskin
De Sam Raskin
De Peter Scholze , Laurent Fargues
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Jean-François Dat
De Jessica Fintzen
De Peter Scholze , Laurent Fargues
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Jessica Fintzen
De Jean-François Dat
De Peter Scholze , Laurent Fargues
De David Ben-Zvi
De Michael Harris , Tony Feng
De Yiannis Sakellaridis
De Michael Harris , Tony Feng
De Yiannis Sakellaridis
De Michael Harris , Tony Feng
De Vasudevan Srinivas
De Marc Levine
