Pieri-type multiplication formula for quantum Grothendieck polynomials
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911930750337024 |
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| author | Naito, Satoshi Sagaki, Daisuke |
| author_facet | Naito, Satoshi Sagaki, Daisuke |
| contents | 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 $QK(Fl_{n})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_01578 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pieri-type multiplication formula for quantum Grothendieck polynomials Naito, Satoshi Sagaki, Daisuke Quantum Algebra Combinatorics Representation Theory Mathematics Subject Classification 2020: Primary 05E05, 05E14, Secondary 14M15, 14N35, 14N15 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 $QK(Fl_{n})$. |
| title | Pieri-type multiplication formula for quantum Grothendieck polynomials |
| topic | Quantum Algebra Combinatorics Representation Theory Mathematics Subject Classification 2020: Primary 05E05, 05E14, Secondary 14M15, 14N35, 14N15 |
| url | https://arxiv.org/abs/2211.01578 |