arXiv math/04092062004-09math.QA

Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups

Yuri Bazlov

备注：: v2: New section added where the nilCoxeter algebra is realised in the Nichols-Woronowicz algebra; switched from left to (more convenient) right braided partial derivatives; references and acknowledgments added
发表信息：: J. Algebra 297 (2006), no. 2, 372--399

英文摘要：

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 algebra in the Yetter-Drinfeld category over W. This gives a braided Hopf algebra version of the corresponding Schubert calculus. Our proof is based on methods of braided differential calculus rather than on working directly with the relations in the Nichols algebra, which are not known explicitly. We also discuss the relationship between Fomin-Kirillov quadratic algebras, Kirillov-Maeno bracket algebras and our construction.

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