Pieri-type multiplication formula for quantum Grothendieck polynomials

2022/11/03 by Satoshi Naito, Naito, Satoshi, Daisuke Sagaki +1 · 1 citation
Mathematics · #05E14 #14N15 #14N35 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Mathematics Subject Classification 2020: Primary 05E05 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary 14M15

paper · pdf · doi:10.48550/arxiv.2211.01578

openalex publication_date 2022/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Cited by

• Toward quantum Pieri rule for Fℓ_n via Seidel representation

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• Quantum Grothendieck Polynomials
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