# Does there exist a sequence of groups whose representation theory is described by plane partitions?

More precisely, does there exist a sequence G1 < G2 < ... of finite groups such that the irreducible representations of Gn are parameterized by the plane partitions of total size n?

• You'd probably like to have the analogue of the branching rule hold as well, I imagine. – Reid Barton Oct 16 '09 at 18:35
• Yes, that would be ideal. – Qiaochu Yuan Oct 16 '09 at 18:46
• More generally, what are some objects naturally parameterized by plane partitions? I ask this question, because ordinary partitions seems to be a ubiquitous index set. – Dan Flath May 3 '15 at 12:45