The nil Hecke ring and Deodhar's conjecture on Bruhat intervals

DOI10.1007/BF01231299zbMath0813.20043WikidataQ123201201 ScholiaQ123201201MaRDI QIDQ1802545

Matthew J. Dyer

Publication date: 17 June 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144089

zbMATH Keywords

Bruhat orderreflectionslength functionCoxeter systemnil Hecke ring

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Simple, semisimple, reductive (super)algebras (17B20)

Related Items

Tangent cones to Schubert varieties in types \(A_{n}\), \(B_{n}\) and \(C_{n}\), The nil Hecke ring and singularity of Schubert varieties, Affine nil-Hecke algebras and quantum cohomology, The combinatorics of Coxeter categories, On tangent cones to Schubert varieties in type \(E\), Parity sheaves, moment graphs and the \(p\)-smooth locus of Schubert varieties, The Bruhat order, the lookup conjecture and spiral Schubert varieties of type \(\tilde{A}_2\), Kostant-Kumar polynomials and tangent cones to Schubert varieties for involutions in \(A_{n}\), \(F_{4}\), and \(G_{2}\), The multiplicity one case of Lusztig's conjecture., On cones tangent to Schubert varieties of type $D_n$, The smooth loci of spiral Schubert varieties of type A ̃ 2 $$\widetilde{A}_{2}$$, On the combinatorics of \(B\times B\)-orbits on group compactifications, Classes d'Euler équivariantes et points rationnellement lisses. (Equivariant Euler classes and rationally smooth points.), Casselman’s Basis of Iwahori Vectors and Kazhdan–Lusztig Polynomials, Smoothness of Schubert varieties via patterns in root subsystems, On Zariski tangent spaces of Schubert varieties, and a proof of a conjecture of Deodhar, Rational smoothness and fixed points of torus actions, Smoothness of Schubert varieties indexed by involutions in finite simply laced types, Towards combinatorial invariance for Kazhdan-Lusztig polynomials, Twisted filtrations of Soergel bimodules and linear Rouquier complexes

Cites Work

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• The nil Hecke ring and cohomology of \(G/P\) for a Kac-Moody group \(G\)
• Singular locus of a Schubert variety
• Local poincaré duality and non-singularity of schubert varieties
• On the root system of a coxeter group
• Endomorphisms of linear algebraic groups