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#### Equivariant quantum cohomology of the Grassmannian via the rim hook rule

##### External Resource

http://alco.centre-mersenne.org/item/ALCO_2018__1_3_327_0

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##### Fulltext (public)

arXiv:1403.6218.pdf

(Preprint), 524KB

Bertiger-Milicevic-Taipale_Equivariant quantum cohomoloy of the Grassmannian via the rim hook rule_2018.pdf

(Publisher version), 847KB

##### Supplementary Material (public)

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##### Citation

Bertiger, A., Milićević, E., & Taipale, K. (2018). Equivariant quantum cohomology
of the Grassmannian via the rim hook rule.* Algebraic Combinatorics,* *1*(3),
327-352. Retrieved from http://arxiv.org/abs/1403.6218.

Cite as: https://hdl.handle.net/21.11116/0000-0003-D8B7-B

##### Abstract

A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the product of two classes in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provided a way to compute quantum products of Schubert classes in the Grassmannian of k-planes in complex n-space by doing classical multiplication and then applying a combinatorial rim hook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule then gives an effective algorithm for computing all equivariant quantum

Littlewood-Richardson coefficients. Interestingly, this rule requires a

specialization of torus weights modulo n, suggesting a direct connection to the

Peterson isomorphism relating quantum and affine Schubert calculus.

Littlewood-Richardson coefficients. Interestingly, this rule requires a

specialization of torus weights modulo n, suggesting a direct connection to the

Peterson isomorphism relating quantum and affine Schubert calculus.