Quantum cohomology of partial flag manifolds

We give elementary geometric proofs of the structure theorems for the (small) quantum cohomology of partial flag varieties SL⁡(n)/P\operatorname {SL}(n)/P, including the quantum Pieri and quantum Giambelli formulas and the presentation.

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2005-02, Vol.357 (2), p.443-458
Main Author: Buch, Anders Skovsted
Format: Article
Language:English
Subjects:
Algebra
Algebraic combinatorics
Algebraic geometry
Combinatorics
Combinatorics. Ordered structures
Curves
Exact sciences and technology
Increasing sequences
Integers
Mathematical lattices
Mathematical manifolds
Mathematical rings
Mathematical theorems
Mathematics
Polynomials
Research article
Sciences and techniques of general use
Symmetry
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Description
Summary:We give elementary geometric proofs of the structure theorems for the (small) quantum cohomology of partial flag varieties SL⁡(n)/P\operatorname {SL}(n)/P, including the quantum Pieri and quantum Giambelli formulas and the presentation.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-04-03655-4