Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties
2025/04/10 by Amini, Kamyar, Huq-Kuruvilla, Irit, Mihalcea, Leonardo C. +2 · 2 citations
#05E05 #14M15 #14N35 #37K10 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2504.07412
Abstract
We prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety \rm Fl(r1, …, rk;n). The proof relies on pushing forward the Toda presentation obtained by Maeno, Naito and Sagaki for the complete flag variety \rm Fl(n), via Kato's \rm KT(\rm pt)-algebra homomorphism from the quantum K ring of \rm Fl(n) to that of \rm Fl(r1, …, rk;n). Starting instead from the Whitney presentation for \rm Fl(n), 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 \rm Fl(n), following Anderson, Chen, and Tseng, which is based on the fact that the \rm K-theoretic J-function is an eigenfunction of the finite difference Toda Hamiltonians.
Citations
- A Nakayama result for the quantum K theory of homogeneous spaces
- Quantum K-theoretic divisor axiom for flag manifolds
- Borel-type presentation of the torus-equivariant quantum K-ring of flag manifolds of type C
- Quantum K-Rings of Partial Flag Varieties, Coulomb Branches, and the Bethe Ansatz
- Quantum K-invariants via Quot schemes I
- Relations in Twisted Quantum K-Rings
- Quantum K Whitney relations for partial flag varieties
- A presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, Part II: quantum double Grothendieck polynomials
- A presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, Part I: the defining ideal
- Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles
- Positivity of minuscule quantum K-theory
- Quantum K-theory of G/P and K-homology of affine Grassmannian
- A general Chevalley formula for semi-infinite flag manifolds and quantum K-theory
- On quantum K-groups of partial flag manifolds
- Loop structure on equivariant K-theory of semi-infinite flag manifolds
- On the finiteness of quantum K-theory of a homogeneous space
- On the quantum K-ring of the flag manifold
- Quantum K-theory of Quiver Varieties and Many-Body Systems
- A conjectural Peterson isomorphism in K-theory
- Peterson Isomorphism in K-theory and Relativistic Toda Lattice
- A Chevalley formula for the equivariant quantum K-theory of cominuscule varieties
- Quantum Integrability and Generalised Quantum Schubert Calculus
- Factorial P- and Q-Schur functions represent equivariant quantum Schubert classes
- Reconstruction and Convergence in Quantum K-Theory via Difference Equations
- Rationality of some Gromov-Witten varieties and application to quantum K-theory
- Quantum K-theory of Grassmannians
- Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups
- Quantum K-Theory I: Foundations
- Quantum K -theory, I: Foundations
- On the WDVV-equation in quantum K-theory
- Whittaker functions on quantum groups and q-deformed Toda operators
- Quantum multiplication of Schur polynomials
- Flags, Schubert polynomials, degeneracy loci, and determinantal formulas
Cited by
Related