Geodesic
An update on Haiman’s conjectures
Forum of Mathematics, Sigma, Tome 12 (2024)

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We revisit Haiman’s conjecture on the relations between characters of Kazdhan–Lusztig basis elements of the Hecke algebra over $S_n$. The conjecture asserts that, for purposes of character evaluation, any Kazhdan–Lusztig basis element is reducible to a sum of the simplest possible ones (those associated to so-called codominant permutations). When the basis element is associated to a smooth permutation, we are able to give a geometric proof of this conjecture. On the other hand, if the permutation is singular, we provide a counterexample. 
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     author = {Alex Corr\^ea Abreu and Antonio Nigro},
     title = {An update on {Haiman{\textquoteright}s} conjectures},
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Alex Corrêa Abreu; Antonio Nigro. An update on Haiman’s conjectures. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.86

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