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On D. Peterson's presentation of quantum cohomology of $G/P$

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arxiv 2210.17382 v3 pith:YEOUZLYB submitted 2022-10-31 math.AG math-phmath.MPmath.RT

classification math.AGmath-phmath.MPmath.RT
keywords petersoncohomologyisomorphismquantumschemeassociatedconstructedcoordinate
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abstract

We prove in full generality that the $T$-equivariant quantum cohomology of any flag variety $G/P$ is isomorphic to the coordinate ring of a stratum of the Peterson scheme associated to the Langlands dual group scheme $G^{\vee}$. This result was discovered by Dale Peterson but remains unpublished. Our isomorphism is constructed using Yun-Zhu's isomorphism and Peterson-Lam-Shimozono's homomorphism.

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  1. Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$

    math.AG 2025-09 conditional novelty 7.0 of 10

    The quantum cohomology of the smooth Schubert divisor X_{w0 s_{n-1}} in Fl_n is presented, with a quantum Chevalley formula and quantum Schubert polynomials identical to those of Fl_n.

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