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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Humphreys, Reflection Groups and Coxeter Groups, Cambridge Stud
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Combinatorial algorithm extends classical Lie algebra methods to compute GK dimensions for highest weight modules over sl(m|n) and osp(2|2n), showing dependence only on the even part.
Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
Five equivalent characterizations of strong Δ-matroids are given, including novel peerless and isolated antipode conditions that yield new local exchange axioms, motivated by tropical equations from the orthogonal Grassmannian.
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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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Gelfand--Kirillov dimensions of highest weight modules for basic classical Lie superalgebras
Combinatorial algorithm extends classical Lie algebra methods to compute GK dimensions for highest weight modules over sl(m|n) and osp(2|2n), showing dependence only on the even part.
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Orlik--Solomon sheaf homology of geometric lattices
Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
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Characterisations of strong $\Delta$-matroids
Five equivalent characterizations of strong Δ-matroids are given, including novel peerless and isolated antipode conditions that yield new local exchange axioms, motivated by tropical equations from the orthogonal Grassmannian.
- Rational Weyl group elements of odd type D