Huge 5 feet shoe rack which is fixed to the common area wall is acceptable by the law or not

First, express your displeasure by means of complaint to Society and seek the rules under which such common area is permissible, and action was taken by them to discourage such inconvenient acts, spoiling the relations between neighbours.   Depending on their response report to Sub-Registrar.  Please understand the need for maintaining good neighbourly relations as both of you have to be in the same place for many years in future and express your objections to the owner in a polite and decent manner first.

The Law states that " 

All open /common spaces meant for use of all members eg, staircase, steps, landing areas, parking areas, lift, corridor, and such other spaces, cannot be occupied by any member for his own use. The use of such areas shall be restricted to the cause for which these are meant."

However, it will be prudent to settle the matter amicably, it is not advisable to take recourse to legal remedy against a neighbour.