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Generalized Local Coefficients by De la Mora, Carlos; Stevens, Shaun is a scholarly article available to read on EtoBox.

What is Generalized Local Coefficients about?

In this paper we showed that under two assumptions we are able to define interesting functions that we call generalized local coefficients. We showed that in the quasi-split case generalized local coefficients are up to a positive constant the same as Shahidi's local coefficients. We provide a proof that the non quasi-split group $GL_m(D)$, for a central division algebra $D$ satisfies those assumptions. We also showed that generalized local coefficients satisfy nice properties, like the relation to Plancherel measures and multiplicativity inherited by that of intertwining operators. Generalized local coefficients are only defined for representations that are $(Y,\varphi)$-generic which is a generalization of generic representations in the quasi-split case. Here $Y$ denotes a nilpotent element in the Lie algebra of the group and $\varphi$ is a co-character related to $Y$.

Author

De la Mora, Carlos; Stevens, Shaun

Published

2015

Language

EN