Upper and lower bounds for Kazhdan-Lusztig polynomials
The author gives upper and lower bounds for the Kazhdan-Lusztig polynomials of any Coxeter group \(W\) and shows that if \(W\) is finite then the \(k\)th coefficient of the Kazhdan-Lusztig polynomial of two elements \(u\), \(v\) of \(W\) is bounded from above by a polynomial (which depends only on \(k\)) in \(l(v)-l(u)\) for any \(k\geq 0\). This implies the validity of Lascoux-Schützenberger's conjecture for all sufficiently long intervals and gives supporting evidence in favour of the Dyer-Lusztig conjecture.
scientific article; zbMATH DE number 1199950