Index, alter, and references privileges
The Index privilege permits its holder to create and alter indexes on the table. The Index privilege, similar to the Select, Insert, Update, and Delete privileges, is granted automatically to PUBLIC when you create a table.
You can grant the Index privilege to anyone, but to exercise the privilege, the user must also hold the Resource database privilege. So, although the Index privilege is granted automatically (except in ANSI-compliant databases), users who have only the Connect privilege to the database cannot exercise their Index privilege. Such a limitation is reasonable because an index can fill a large amount of disk space.
The Alter privilege permits its holder to use the ALTER TABLE statement on the table, including the power to add and drop columns, reset the starting point for SERIAL columns, and so on. You should grant the Alter privilege only to users who understand the data model well and whom you trust to exercise their power carefully.
The References privilege allows you to impose referential constraints on a table. As with the Alter privilege, you should grant the References privilege only to users who understand the data model well.