Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2025
• Hauptverfasser: Amini, Kamyar, Huq-Kuruvilla, Irit, Mihalcea, Leonardo C., Orr, Daniel, Xu, Weihong
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2025
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/214184
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties. Kamyar Amini, Irit Huq-Kuruvilla, Leonardo C. Mihalcea, Daniel Orr and Weihong Xu. SIGMA 21 (2025), 098, 26 pages

We prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety Fl(₁, …, ₖ; ). The proof relies on pushing forward the Toda presentation obtained by Maeno, Naito, and Sagaki for the complete flag variety Fl(), via Kato's KT(pt)-algebra homomorphism from the quantum K ring of Fl() to that of Fl(₁, …, ₖ; ). Starting instead from the Whitney presentation for Fl(), we show that the same pushforward technique gives a recursive formula for polynomial representatives of quantum K Schubert classes in any partial flag variety which do not depend on quantum parameters. In an appendix, we include another proof of the Toda presentation for the equivariant quantum K ring of Fl(), following Anderson, Chen, and Tseng, which is based on the fact that the K-theoretic J-function is an eigenfunction of the finite difference Toda Hamiltonians.