Offline multidimensional RMQ/RSQ in query model
So, you are interested in range queries in the "dense case" (an array) as opposed to the case most frequently studied in theory (arbitrary points in space).

The RMQ problem is easier than the semigroup sum problem, and no $\alpha$ is needed. The most recent result I know is: Hao Yuan, Mikhail J. Atallah: Data Structures for Range Minimum Queries in Multidimensional Arrays, SODA 2010

The semigroup sum problem is mainly of theoretical interest, in my opinion (what is a natural semigroup beyond max?). This explains why the Chazelle-Rosenberg paper does not have a lot of citations.