# nt.quantity principle – Automorphy issue and the determinant of the Jacobian matrix Answer

Hello pricey customer to our community We will proffer you an answer to this query nt.quantity principle – Automorphy issue and the determinant of the Jacobian matrix ,and the respond will breathe typical by means of documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning in regards to the respond to this query.

nt.quantity principle – Automorphy issue and the determinant of the Jacobian matrix

There are two cocycles defining the automorphy elements.

Let $$D$$ breathe the bounded symmetric province (because of Harish-Chandra). Then there’s a canonical automorphy issue $$J:Gtimes Dto K_{mathbb{C}}$$ the place $$G$$ is a actual Lie group with a maximal compact subgroup $$Ok$$, $$D=G/Ok$$ and $$K_{mathbb{C}}$$ is the complexification of $$Ok$$.

Meanwhile, because of Baily and Borel, there may be too an automorphy issue $$J_0:Gtimes Dto mathbb{C}^{*}$$ coming from the determinant of the Jacobian matrix, i.e. the Jacobian of the motion of $$g$$ at $$zin D$$.(Baily, Walter L., and Armand Borel. “Compactification of arithmetic quotients of bounded symmetric domains.” Annals of arithmetic (1966): 442-528.)

Is there any relation between these two? The first one appears extra common to me since we are able to add the illustration of $$K_{mathbb{C}}$$ whereas the second is at all times a nonzero complicated quantity. And with the primary one, we are able to switch the automorphic kinds (vector-valued) on Lie teams to those outlined on the province.

we are going to proffer you the answer to nt.quantity principle – Automorphy issue and the determinant of the Jacobian matrix query through our community which brings all of the solutions from a number of dependable sources.