Subalgebras of the Fomin-Kirillov algebra

DOI10.1007/s10801-016-0688-4zbMath1350.05179arXiv1310.4112OpenAlexW1770982736WikidataQ57429893 ScholiaQ57429893MaRDI QIDQ345158

Karola Mészáros, Ricky Ini Liu, Jonah Blasiak

Publication date: 25 November 2016

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.4112

zbMATH Keywords

Coxeter groupNichols algebraFomin-Kirillov algebranil-Coxeter algebra

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items

Positive expressions for skew divided difference operators, A decomposition Theorem for pointed braided Hopf algebras, On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials, On the commutative quotient of Fomin-Kirillov algebras, PBW deformations of a Fomin-Kirillov algebra and other examples, On the quadratic dual of the Fomin–Kirillov algebras

Uses Software

• BERGMAN

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Schur times Schubert via the Fomin-Kirillov algebra
• Cyclage, catabolism, and the affine Hecke algebra.
• Alcove walks, Hecke algebras, spherical functions, crystals and column strict tableaux.
• The based ring of the lowest two-sided cell of an affine Weyl group
• Hecke algebras and Jantzen's generic decomposition patterns
• A Weyl group generation function that ought to be better known
• A combinatorial bijection between standard Young tableaux and reduced words of Grassmannian permutations
• Fibered quadratic Hopf algebras related to Schubert calculus
• The \(K\)-theory of the flag variety and the Fomin--Kirillov quadratic algebra
• Noncommutative algebras related with Schubert calculus on Coxeter groups
• Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups.
• Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent
• Combinatorics of Coxeter Groups
• Alcove path and Nichols-Woronowicz model of the equivariant K-theory of generalized flag varieties
• Freeness of hopf algebras over coideal subalgebras
• Bialgebras of type one^*
• ON SOME ALGEBRAIC AND COMBINATORIAL PROPERTIES OF DUNKL ELEMENTS