Rajan Sundaravaradhan’s research while affiliated with Amrita Vishwa Vidyapeetham and other places

In this article we prove the equality of two different centralizers which appear in the calculation of local coefficients, the main tool in defining local root numbers from Langlands–Shahidi method. More precisely, we prove the main Assumption 4.1 in establishing Theorem 6.1 of [20] in the case of quasi-split groups, a result which is necessary in establishing stability of root numbers upon twists by highly ramified characters, the main impediment in establishing functoriality from this method.