Pith. sign in

REVIEW 2 cited by

A presentation of the torus-equivariant quantum $K$-theory ring of flag manifolds of type $A$, Part I: the defining ideal

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2302.09485 v4 pith:PJCVZ22D submitted 2023-02-19 math.QA math.AGmath.COmath.KTmath.RT

classification math.QAmath.AGmath.COmath.KTmath.RT
keywords torus-equivariantflagmanifoldspresentationquantumringnon-equivarianttheory
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We give a presentation of the torus-equivariant quantum $K$-theory ring of flag manifolds of type $A$, as a quotient of a polynomial ring by an explicit ideal. This is the torus-equivariant version of our previous result, which gives a presentation of the non-equivariant quantum $K$-theory ring of flag manifolds of type $A$. However, the method of proof for the torus-equivariant one is completely different from that for the non-equivariant one; our proof is based on the result in the $Q = 0$ limit, and uses Nakayama-type arguments to upgrade it to the quantum situation. Also, in contrast to the non-equivariant case in which we used the Chevalley formula, we make use of the inverse Chevalley formula for the torus-equivariant $K$-group of semi-infinite flag manifolds to obtain a relation which yields our presentation.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum K-theory levels in physics and math

    hep-th 2025-06 conditional novelty 6.0 of 10

    Chern-Simons levels and Ruan-Zhang levels are identified as the same twisting of quantum K-theory, with Coulomb branch equations matching difference operator symbols and geometric windows matching mirror triviality.

  2. Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\beta$-Grothendieck polynomials

    math-ph 2025-02 conditional novelty 6.0 of 10

    Bethe ansatz states of a new GL(n) five vertex model expand into double β-Grothendieck polynomials, and the model's Bethe equations reproduce the quantum Whitney relations of flag varieties.

Pith tools