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Pieri-type multiplication formula for quantum Grothendieck polynomials

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arxiv 2211.01578 v4 pith:VJN2QN62 submitted 2022-11-03 math.QA math.COmath.RT

Satoshi Naito , Daisuke Sagaki This is my paper · ORCID
classification math.QAmath.COmath.RT
keywords quantumformulagrothendieckpolynomialsclassesmultiplicationoppositepieri-type
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abstract

The purpose of this paper is to prove a Pieri-type multiplication formula for quantum Grothendieck polynomials, which was conjectured by Lenart-Maeno. This formula would enable us to compute explicitly the quantum product of two arbitrary (opposite) Schubert classes in the (small) quantum $K$-theory ring $QK(Fl_{n})$ of the (full) flag manifold $Fl_{n}$ of type $A_{n-1}$ on the basis of the fact that quantum Grothendieck polynomials represent (opposite) Schubert classes in $QK(Fl_{n})$.

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  1. Toward quantum Pieri rule for $F\ell_n$ via Seidel representation

    math.AG 2025-07 conditional novelty 4.0 of 10

    In quantum cohomology of the complete flag variety, the special Schubert class acts as a cyclic permutation operator with a quantum monomial weight, and the same is conjectured for quantum K-theory.

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