Time: 16:00-17:00, Wednesday, April 16  

Title: Higher Ext between locally analytic generalized Steinberg with application to higher L invariants for GL(n)

Speaker: Zicheng Qian (Chinese Academy of Sciences)

Abstract: The definition/study of L invariants via locally analytic representation theory has been initiated by Breuil in the case of GL(2,Q_p). The GL(3,Q_p) case has been studied extensively by Schraen and Breuil–Ding from different aspects. Motivated by their work and Gehrmann's work on automorphic L invariants, it is clear that understanding higher Ext groups between various locally analytic generalized Steinberg is crucial to develop the theory of (higher) L invariants for GL(n). A key example of such Ext groups is Ext_G^{n-1}(1,St_G^{an}) (*) with G=PGL(n,K) and St_G^{an} being the locally analytic Steinberg representation of G. We would first present a list of results on the structure of (*) which technically depends on the interpretation of top primitive class of sl_n using relative Lie algebra cohomology w.r.t. sl_{n-1}. Then we discuss how the theory of higher L invariants for GL(n) is essentially equivalent to an isomorphism between (*) and certain Galois Ext^1 group. Finally we consider some canonical subspaces of both (*) and its Galois counterpart, and discuss how such isomorphism might be explicitly characterized.