Nichols–Woronowicz algebra model for Schubert calculus on Coxeter groups

By Yuri Bazlov. 2004

68 citations recorded by the source corpus.

Abstract We realise the cohomology ring of a flag manifold, more generally the coinvariant algebra of an arbitrary finite Coxeter group W, as a commutative subalgebra of a certain Nichols–Woronowicz algebra in the Yetter–Drinfeld category over W. This gives a braided Hopf algebra version of the corresponding Schubert calculus. The nilCoxeter algebra and its action on the coinvariant algebra by divided difference operators are also realised in the Nichols–Woronowicz algebra. We discuss the relationship between Fomin–Kirillov quadratic algebras, Kirillov–Maeno bracket algebras and our construction.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

István Heckenberger

In Geometry and Topology

Citations in the corpus

Classification of arithmetic root systems (2006, background): “Further, Bazlov [8] proved that the cohomology ring of a flag variety can be considered as a subalgebra of a particular Nichols algebra of nonabelian group type.”