# TR-2007-14

## Geometric Complexity Theory VII: Nonstandard quantum group for the plethysm problem

Ketan D. Mulmuley. 4 September, 2007.

Communicated by Ketan Mulmuley.

**Obsolete:** Yes *(updated 12/19/12)*

### Abstract

This article describes a nonstandard quantum group
that may be used to derive a positive formula
for the plethysm problem,
just as the standard (Drinfeld-Jimbo) quantum group
can be used to derive the positive
Littlewood-Richardson rule for arbitrary complex semisimple Lie groups.
The sequel GCT8 gives conjecturally correct algorithms to
construct canonical bases of the coordinate rings of these nonstandard
quantum groups and canonical bases of the dually paired
nonstandard deformations of the symmetric group algebra.
A positive $\#P$-formula for the plethysm constant follows from the
conjectural properties of these canonical bases and the
duality and reciprocity conjectures herein.

### Original Document

The original document is available in Postscript (uploaded 4 September, 2007 by
Ketan Mulmuley).