dorsal/arxiv
View Schemaspl(p,q) superalgebra and differential operators
| Authors | Yves Brihaye, Stefan Giller, Piotr Kosinski |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710018 |
| URL | https://arxiv.org/abs/q-alg/9710018 |
Abstract
Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general ingredients necessary to construct these representations and present examples related to spl(2,1) and spl(2,2). By revisiting the products of projectivised representations of sl(2), we are able to construct new sets of differential operators preserving some space of polynomials in two or more variables. In particular, this allows to express the representation of spl(2,1) in terms of matrix differential operators in two variables. The corresponding operators provide the building blocks for the construction of quasi exactly solvable systems of two and four equations in two variables. We also present a quommutator deformation of spl(2,1) which, by construction, provides an appropriate basis for analyzing the quasi exactly solvable systems of finite difference equations.
{
"annotation_id": "65510816-4d39-42d9-9031-fee4ae445419",
"date_created": "2026-03-02T18:01:28.845000Z",
"date_modified": "2026-03-02T18:01:28.845000Z",
"file_hash": "0a00afe14dee393efd4d1fb16589c9f9bd5ad7c7ec5a2679b1040fd9b92309ad",
"private": false,
"record": {
"abstract": "Series of finite dimensional representations of the superalgebras spl(p,q)\ncan be formulated in terms of linear differential operators acting on a\nsuitable space of polynomials. We sketch the general ingredients necessary to\nconstruct these representations and present examples related to spl(2,1) and\nspl(2,2). By revisiting the products of projectivised representations of sl(2),\nwe are able to construct new sets of differential operators preserving some\nspace of polynomials in two or more variables. In particular, this allows to\nexpress the representation of spl(2,1) in terms of matrix differential\noperators in two variables. The corresponding operators provide the building\nblocks for the construction of quasi exactly solvable systems of two and four\nequations in two variables. We also present a quommutator deformation of\nspl(2,1) which, by construction, provides an appropriate basis for analyzing\nthe quasi exactly solvable systems of finite difference equations.",
"arxiv_id": "q-alg/9710018",
"authors": [
"Yves Brihaye",
"Stefan Giller",
"Piotr Kosinski"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "spl(p,q) superalgebra and differential operators",
"url": "https://arxiv.org/abs/q-alg/9710018"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "31060e8e-ebe1-4772-851b-719535416ad5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}