An Auslander-Gorenstein ring is a noetherian ring R that has finite left and right selfinjective dimension and such that $fd(I_i) \leq i$ for all $i \geq 0$ for an injective coresolution of the regular module $R$ ($fd(M)$ denotes the flat dimension of a module $M$).
A module M over an Auslander-Gorenstein algebra with $id(R)=g$ is called holonomic in case $Ext_R^i(M,R)=0$ for $i=0,1,...,g-1$ and $Ext_R^g(M,R) \neq 0$.
Questions: 1. Who named such modules as holonomic modules and what is the reason/motivation?
For the Weyl algebra the "classical holonomic modules" as defined for example in chapter 10 in the book "A Primer of Algebraic D-Modules" by Coutinho should coincide with the here defined holonomic modules (maybe this is the motivation for the name in general?). Is there a reference for this and where was this first proven?
For which Auslander-Gorenstein algebra has the class of holonomic modules been considered (besides the Weyl algebra) with a complete classification or interesting results?
Are there recent results/open problems on holonomic modules or an overview article?
