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arxiv:2303.13695
On the minimal power of q in a Kazhdan-Lusztig polynomial
Published on Mar 23, 2023
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Abstract
The paper provides an exact formula for the smallest positive power in Kazhdan-Lusztig polynomials and a tight upper bound on the exponent in simply-laced types, resolving a 2002 conjecture.
AI-generated summary
For w in the symmetric group, we provide an exact formula for the smallest positive power q^{h(w)} appearing in the Kazhdan-Lusztig polynomial P_{e,w}(q). We also provide a tight upper bound on h(w) in simply-laced types, resolving a conjecture of Billey-Postnikov from 2002.
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