A Note on Quantization Operators on Nichols Algebra Model for Schubert Calculus on Weyl groups

2004/12/31 by Anatol N. Kirillov, Anatol. N. Kirillov, Toshiaki Maeno · 4 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Commutative property #Flag (linear algebra) #Quantum algebra #Schubert calculus #Schubert variety #Subalgebra #Tensor product #Variety (cybernetics) #math.QA

paper · pdf · doi:10.1007/s11005-005-7649-5

published in Letters in Mathematical Physics 72(3), 233-241 (Springer Science+Business Media)

arxiv created 2005/03/11 · openalex publication_date 2005/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We give a description of the (small) quantum cohomology ring of the flag variety as a certain commutative subalgebra in the tensor product of the Nichols algebras. Our main result can be considered as a quantum analog of a result by Y. Bazlov.

Citations

• Differential calculus on compact matrix pseudogroups (quantum groups)
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• Quantum cohomology of flag manifolds and Toda lattices