dorsal/arxiv
View Schema(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula
| Authors | Andrei Okounkov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9605013 |
| URL | https://arxiv.org/abs/q-alg/9605013 |
Abstract
We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We obtain two explicit formulas for these polynomials: a $q$-integral representation and a combinatorial formula. Our main tool is a $q$-integral representation for ordinary Macdonald polynomials. We also discuss duality for shifted Macdonald polynomials and Jack degeneration of these polynomials.
{
"annotation_id": "97c61109-c333-447f-aa8a-c36473b64a9d",
"date_created": "2026-03-02T18:01:28.591000Z",
"date_modified": "2026-03-02T18:01:28.591000Z",
"file_hash": "c4bd61ddadb0ca14bbd7c4d3bb47fd55191edf078ee6c02073dc076a2d842c0b",
"private": false,
"record": {
"abstract": "We extend some results about shifted Schur functions to the general context\nof shifted Macdonald polynomials. We obtain two explicit formulas for these\npolynomials: a $q$-integral representation and a combinatorial formula. Our\nmain tool is a $q$-integral representation for ordinary Macdonald polynomials.\nWe also discuss duality for shifted Macdonald polynomials and Jack degeneration\nof these polynomials.",
"arxiv_id": "q-alg/9605013",
"authors": [
"Andrei Okounkov"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula",
"url": "https://arxiv.org/abs/q-alg/9605013"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "aa0d9684-9371-4684-af18-21d4348f8ac5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}