On quantum cohomology rings of partial flag varieties
نویسندگان
چکیده
منابع مشابه
On Quantum Cohomology Rings of Partial Flag Varieties
0. Introduction. The main goal of this paper is to give a unified description for the structure of the small quantum cohomology rings for all projective homogeneous spaces SLn(C)/P , where P is a parabolic subgroup. The quantum cohomology ring of a smooth projective variety, or more generally of a symplectic manifoldX, has been introduced by string theorists (see [Va] and [W1]). Roughly speakin...
متن کامل. A G ] 6 O ct 1 99 7 ON QUANTUM COHOMOLOGY RINGS OF PARTIAL FLAG VARIETIES
The main goal of this paper is to give a unified description for the structure of the small quantum cohomology rings for all homogeneous spaces of SL n (C). The quantum cohomology ring of a smooth projective variety, or, more generally of a symplectic manifold, has been introduced by physicists in the study of topo-logical field theories ([V], [W]). In the past few years, the highly non-trivial...
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We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263–277). We also give a geometric proof of the quantum Monk formula.
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Cohomological induction gives an algebraic method for constructing representations of a real reductive Lie group G from irreducible representations of reductive subgroups. Beilinson-Bernstein localization alternatively gives a geometric method for constructing Harish-Chandra modules for G from certain representations of a Cartan subgroup. The duality theorem of Hecht, Miličić, Schmid and Wolf e...
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We give elementary geometric proofs of the structure theorems for the (small) quantum cohomology of partial flag varieties SL(n)/P , including the quantum Pieri and quantum Giambelli formulas and the presentation.
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 1999
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-99-09815-0