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.
Calculating thep-canonical basis of Hecke algebras
5 Pith papers cite this work. Polarity classification is still indexing.
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Extends Lusztig total positivity to symmetric spaces G/K via Hausdorff closure, proves cell decomposition with positive parametrizations and subtraction-free transitions.
MCS spaces are CS sets whose MCS stratification coincides with the intrinsic stratification.
Instanton partition functions on the blow-up are given by chamber-dependent contour integrals over super-partitions selected by stability conditions, yielding explicit wall-crossing formulas that recover the Nakajima-Yoshioka blow-up formula.
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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.
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Total positivity and symmetric spaces
Extends Lusztig total positivity to symmetric spaces G/K via Hausdorff closure, proves cell decomposition with positive parametrizations and subtraction-free transitions.
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MCS Spaces are CS
MCS spaces are CS sets whose MCS stratification coincides with the intrinsic stratification.
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Wall-crossing of Instantons on the Blow-up
Instanton partition functions on the blow-up are given by chamber-dependent contour integrals over super-partitions selected by stability conditions, yielding explicit wall-crossing formulas that recover the Nakajima-Yoshioka blow-up formula.
- Algebraic cobordism rings of wonderful varieties and matroids