{"paper":{"title":"Shifted quantum toroidal algebra of type $\\mathfrak{gl}_{1|1}$ and the Pieri rule of the super Macdonald polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The action of super charges from the shifted quantum toroidal algebra of type gl_{1|1} implies the Pieri rule for super Macdonald polynomials.","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Hiroaki Kanno, Jun'ichi Shiraishi, Ryo Ohkawa","submitted_at":"2026-05-16T02:50:52Z","abstract_excerpt":"The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module (combinatorial representation) of the quantum toroidal algebra $\\mathcal{U}_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_{1|1})$. The action of the super charges of $\\mathcal{U}_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_{1|1})$ implies the Pieri rule of the super Macdonald polynomials. We can express the Pieri rule in terms of differential operators in the power sums $p_k$ and the fermionic power sums $\\pi_k$, which leads to the operators on the Fock space of a free boson and a free fermio"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The action of the super charges of U_{q,t}(widehat{widehat{gl}}_{1|1}) implies the Pieri rule of the super Macdonald polynomials.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module of the quantum toroidal algebra.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Super Macdonald polynomials indexed by super partitions form a basis of the level zero super Fock module of the shifted quantum toroidal algebra U_{q,t}(gl hat 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