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Geometry of Peterson Schubert calculus in type A and left-right diagrams
Abe, Hiraku1; Horiguchi, Tatsuya2; Kuwata, Hideya3; Zeng, Haozhi4
1 Okayama University of Science Faculty of Science, Department of Applied Mathematics 1-1 Ridai-cho Kita-ku Okayama 700-0005 Japan
2 National institute of technology Ube college 2-14-1 Tokiwadai Ube Yamaguchi 755-8555 Japan
3 Kindai University Technical College 7-1 Kasugaoka, Nabari Mie 518-0459 Japan
4 Huazhong University of Science and Technology School of Mathematics and Statistics Wuhan 430074 P.R. China
Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 383-412.

We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the positivity of the structure constants from a geometric viewpoint, and provide a manifestly positive combinatorial formula for them. We also prove that our basis coincides with the additive basis introduced by Harada–Tymoczko.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.342
Classification: 14M15, 05E40
Keywords: Peterson variety, Peterson Schubert calculus

Abe, Hiraku 1; Horiguchi, Tatsuya 2; Kuwata, Hideya 3; Zeng, Haozhi 4

1 Okayama University of Science Faculty of Science, Department of Applied Mathematics 1-1 Ridai-cho Kita-ku Okayama 700-0005 Japan
2 National institute of technology Ube college 2-14-1 Tokiwadai Ube Yamaguchi 755-8555 Japan
3 Kindai University Technical College 7-1 Kasugaoka, Nabari Mie 518-0459 Japan
4 Huazhong University of Science and Technology School of Mathematics and Statistics Wuhan 430074 P.R. China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Geometry of {Peterson} {Schubert} calculus in type {A} and left-right diagrams},
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Abe, Hiraku; Horiguchi, Tatsuya; Kuwata, Hideya; Zeng, Haozhi. Geometry of Peterson Schubert calculus in type A and left-right diagrams. Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 383-412. doi : 10.5802/alco.342. https://alco.centre-mersenne.org/articles/10.5802/alco.342/

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