The degree-shifting action on the cohomology of locally symmetric spaces, which has its origins in archimedean representation theory, enjoys a surprising connection with arithmetic as expected by the so-called motivic action conjectures. On the other hand, in the case of Shimura varieties, the nature of degree-shifting action is subtle, even for modular curves; why complex conjugation? In this talk, we will describe the subtle nature of the degree-shifting action on the coherent cohomology of Shimura varieties, which involves archimedean L-packets. Speaker(s): Gyujin Oh (Princeton University)