Exposing Relative Endoscopy in Unitary Symmetric Spaces
  We introduce a new class of symmetric space orbital integrals important for applications in certain relative trace formulas appearing in the theory of automorphic representations. We verify a fundamental lemma for $U_2\times U_2\hookrightarrow U_4$ via an explicit calculation, showing strong evidence that there is a general theory of endoscopy lurking in this situation. 
Jason K.C. Pol\'ak
math.RT math.NT