The quantum cohomology of flag varieties and the periodicity of the Schubert structure constants |
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Authors: | Izzet Coskun |
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Institution: | 1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607, USA
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Abstract: | We give conditions on a curve class that guarantee the vanishing of the structure constants of the small quantum cohomology
of partial flag varieties F(k
1, ..., k
r
; n) for that class. We show that many of the structure constants of the quantum cohomology of flag varieties can be computed
from the image of the evaluation morphism. In fact, we show that a certain class of these structure constants are equal to
the ordinary intersection of Schubert cycles in a related flag variety. We obtain a positive, geometric rule for computing
these invariants (see Coskun in A Littlewood–Richardson rule for partial flag varieties, preprint). Our study also reveals
a remarkable periodicity property of the ordinary Schubert structure constants of partial flag varieties. |
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Keywords: | |
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