Quantum multiplication through equivariant Schubert calculus
Chi-Kwong Fok
TL;DR
This paper rederives key formulas in quantum Schubert calculus using equivariant cohomology and extends these ideas to obtain new equivariant quantum formulas, highlighting the role of characteristic classes.
Contribution
It introduces a new approach to quantum Schubert calculus by studying equivariant cohomology and derives novel equivariant quantum Giambelli and Pieri formulas.
Findings
Rederived quantum Pieri's formula and rim hook algorithm
Extended to equivariant quantum Schubert calculus
Obtained equivariant quantum Giambelli and Pieri formulas
Abstract
In this note, we rederive quantum Pieri's formula and the rim hook algorithm in quantum Schubert calculus by studying multiplication in the equivariant cohomology ring of Grassmannians with respect to equivariant Schubert classes which are characteristic classes. We also extend this idea in studying equivariant quantum Schubert calculus, and obtain the equivariant quantum Giambelli's and Pieri's formulae in terms of characteristic classes, with the former formula shown to be free of quantum deformation.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications