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.
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.
For odd r >= 5 the rational elements of W(D_r) are w0 together with explicitly described signed cyclic elements c_I and d_I for each non-empty I subset of {1..r-1}, yielding a rationality graph of 2^r-1 vertices that is two Boolean halves glued at w0.
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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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Rational Weyl group elements of odd type D
For odd r >= 5 the rational elements of W(D_r) are w0 together with explicitly described signed cyclic elements c_I and d_I for each non-empty I subset of {1..r-1}, yielding a rationality graph of 2^r-1 vertices that is two Boolean halves glued at w0.