Kazhdan–Lusztig conjectures

In the mathematical field of representation theory, a Kazhdan–Lusztig polynomial $P_{y,w}(q)$ is a member of a family of integral polynomials introduced by David Kazhdan and George Lusztig (1979). They are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group.