Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Peterson-Lam-Shimozono's theorem is an affine analogue of quantum
  Chevalley formula   We give a new proof of an unpublished theorem of Peterson, proved previously
by Lam-Shimozono, which identifies explicitly the structure constants for the
multiplications of Schubert classes in the $T$-equivariant quantum cohomology
$QH_T(G/P)$ of any flag variety $G/P$ with the $T$-equivariant Pontryagin
homology $H^T(Gr_G)$ of the affine Grassmannian $Gr_G$, where $G$ is any simple
complex Lie group. Our approach is to construct an $H_T(pt)$-algebra
homomorphism by Gromov-Witten theory and show that it is equal to Peterson's
map. More precisely, the map is defined via Savelyev's generalized Seidel
representations which can be interpreted as certain Gromov-Witten invariants
with input $H^T(Gr_G)\otimes QH_T(G/P)$. We determine these invariants
completely, in a way similar to how Fulton-Woodward did in their proof of
quantum Chevalley formula.

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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th