{"paper":{"title":"Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Inhomogeneous q-Whittaker polynomials form a basis for a commutative ring extending the symmetric functions to a subring of its completion.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ajeeth Gunna, Damir Yeliussizov","submitted_at":"2026-05-13T12:26:20Z","abstract_excerpt":"We study inhomogeneous $q$-Whittaker polynomials which extend both $q$-Whittaker and stable Grothendieck polynomials. We prove that inhomogeneous $q$-Whittaker polynomials (in countably many variables) form a basis of certain commutative ring extending the ring of symmetric functions to a subring of its completion. We then describe positive specializations of that ring and relate them with a subset of Macdonald-positive specializations of the ring of symmetric functions. We also show some related probability distributions obtained from positive specializations of inhomogeneous $q$-Whittaker po"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"inhomogeneous q-Whittaker polynomials (in countably many variables) form a basis of certain commutative ring extending the ring of symmetric functions to a subring of its completion","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The inhomogeneous q-Whittaker polynomials are defined such that they simultaneously extend q-Whittaker and stable Grothendieck polynomials while satisfying the algebraic relations needed for the ring to be commutative and for the basis property to hold in the completion.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Inhomogeneous q-Whittaker polynomials form a basis for an extended commutative ring of symmetric functions and admit positive specializations related to a subset of Macdonald-positive ones, yielding associated probability distributions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Inhomogeneous q-Whittaker polynomials form a basis for a commutative ring extending the symmetric functions to a subring of its completion.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4c3cd39b3220364c8e43b72741c0d0c420dd9df79ed0b74b5022e5a856925882"},"source":{"id":"2605.13432","kind":"arxiv","version":1},"verdict":{"id":"86928ff0-3437-4e41-ba52-d8791f2e51bf","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:06:37.865082Z","strongest_claim":"inhomogeneous q-Whittaker polynomials (in countably many variables) form a basis of certain commutative ring extending the ring of symmetric functions to a subring of its completion","one_line_summary":"Inhomogeneous q-Whittaker polynomials form a basis for an extended commutative ring of symmetric functions and admit positive specializations related to a subset of Macdonald-positive ones, yielding associated probability distributions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The inhomogeneous q-Whittaker polynomials are defined such that they simultaneously extend q-Whittaker and stable Grothendieck polynomials while satisfying the algebraic relations needed for the ring to be commutative and for the basis property to hold in the completion.","pith_extraction_headline":"Inhomogeneous q-Whittaker polynomials form a basis for a commutative ring extending the symmetric functions to a subring of its completion."},"references":{"count":22,"sample":[{"doi":"","year":2017,"title":"On a family of symmetric rational functions","work_id":"9054ae2c-46be-45ea-a14c-4ed206915d4f","ref_index":1,"cited_arxiv_id":"1410.0976","is_internal_anchor":true},{"doi":"","year":2024,"title":"Inhomogeneous spinq-Whittaker polynomials.Annales de la Faculté des sciences de Toulouse : Mathématiques, 33(1):1–68, 2024.arXiv:2104.01415","work_id":"87152918-a7b2-46b8-9f2a-7801c7843a53","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Cambridge Studies in Advanced Mathematics","work_id":"66c9363f-2f3a-4a44-97b0-4ff89c49a197","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Spin $q$-Whittaker polynomials","work_id":"240b60ca-71f9-4765-9d9c-5e84e2a0beec","ref_index":4,"cited_arxiv_id":"1701.06292","is_internal_anchor":true},{"doi":"","year":2002,"title":"A Littlewood-Richardson rule for the K-theory of Grassmannians","work_id":"73d1279d-66b7-4eb3-83e8-0351914d24c9","ref_index":5,"cited_arxiv_id":"math/0004137","is_internal_anchor":true}],"resolved_work":22,"snapshot_sha256":"6a417ed2dc9f8c7f54600dc237ea2136f7edc48562c1d5f788983927d8319cf6","internal_anchors":9},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}