Lattice paths and Kazhdan-Lusztig polynomials

DOI10.1090/S0894-0347-98-00249-5zbMath0904.20033MaRDI QIDQ4383169

Francesco Brenti

Publication date: 24 March 1998

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Coxeter groupsEulerian posetsCoxeter systemslattice pathsKazhdan-Lusztig polynomialsBruhat orderreflectionsBayer-Billera relationsgeneralized \(h\)-vectors

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items

Combinatorial properties of the Temperley-Lieb algebra of a Coxeter group., Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials, Mask formulas for cograssmannian Kazhdan-Lusztig polynomials., Balanced and Bruhat graphs, Equivalence Classes for the μ-Coefficient of Kazhdan–Lusztig Polynomials inS_n, Quasisymmetric functions and Kazhdan-Lusztig polynomials., Note on the Kazhdan-Lusztig polynomials., Non-negativity properties of \(R\)-polynomials, Special matchings and Kazhdan-Lusztig polynomials, Lattice paths, lexicographic correspondence and Kazhdan-Lusztig polynomials., \(T\)-increasing paths on the Bruhat graph of affine Weyl groups are self-avoiding, Explicit formulae for some Kazhdan-Lusztig polynomials, Kazhdan-Lusztig and \(R\)-polynomials from a combinatorial point of view., Boolean elements in Kazhdan-Lusztig theory., \(P\)-kernels, IC bases and Kazhdan-Lusztig polynomials

Cites Work

• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• Bruhat order of Coxeter groups and shellability
• Representations of Coxeter groups and Hecke algebras
• Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function
• A combinatorial formula for Kazhdan-Lusztig polynomials
• Kazhdan-Lusztig and \(R\)-polynomials from a combinatorial point of view.
• Subdivisions and Local h-Vectors
• Combinatorial Expansions of Kazhdan-Lusztig Polynomials
• Möbius inversion for the Bruhat ordering on a Weyl group
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