Maximizing a quadratic objective over unitriangular bases with non-negative 1+s action recovers the Kazhdan-Lusztig basis for all partitions of n≤7 and is conjectured to do so more generally, while minimization recovers Young's seminormal basis.
Relations between Young’s natural and the Kazhdan-Lusztig representa- tions ofSn
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Kazhdan-Lusztig Basis and Optimization
Maximizing a quadratic objective over unitriangular bases with non-negative 1+s action recovers the Kazhdan-Lusztig basis for all partitions of n≤7 and is conjectured to do so more generally, while minimization recovers Young's seminormal basis.