dorsal/arxiv
View SchemaMulti-parameter deformed and nonstandard $Y(gl_M)$ Yangian symmetry in integrable variants of Haldane-Shastry spin chain
| Authors | B. Basu-Mallick |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9802009 |
| URL | https://arxiv.org/abs/solv-int/9802009 |
| DOI | 10.1143/JPSJ.67.2227 |
Abstract
By using `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax equations for these spin chains allow us to find out the related conserved quantities. However, it turns out that such spin chains also possess a few additional conserved quantities which are apparently not derivable from the Lax equations. Identifying these additional conserved quantities, and the usual ones related to Lax equations, with different modes of a monodromy matrix, it is shown that the above mentioned HS like spin chains exhibit multi-parameter deformed and `nonstandard' variants of $Y(gl_M)$ Yangian symmetry.
{
"annotation_id": "4c7ac383-cee6-4633-9538-86cf96d31baf",
"date_created": "2026-03-02T18:02:51.396000Z",
"date_modified": "2026-03-02T18:02:51.396000Z",
"file_hash": "8707e0f28d2c1f7ff7693e6bb20dd4b32000d6cb3388be52fca83c67ebd0e5d0",
"private": false,
"record": {
"abstract": "By using `anyon like\u0027 representations of permutation algebra, which pick up\nnontrivial phase factors while interchanging the spins of two lattice sites, we\nconstruct some integrable variants of Haldane-Shastry (HS) spin chain. Lax\nequations for these spin chains allow us to find out the related conserved\nquantities. However, it turns out that such spin chains also possess a few\nadditional conserved quantities which are apparently not derivable from the Lax\nequations. Identifying these additional conserved quantities, and the usual\nones related to Lax equations, with different modes of a monodromy matrix, it\nis shown that the above mentioned HS like spin chains exhibit multi-parameter\ndeformed and `nonstandard\u0027 variants of $Y(gl_M)$ Yangian symmetry.",
"arxiv_id": "solv-int/9802009",
"authors": [
"B. Basu-Mallick"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"doi": "10.1143/JPSJ.67.2227",
"title": "Multi-parameter deformed and nonstandard $Y(gl_M)$ Yangian symmetry in integrable variants of Haldane-Shastry spin chain",
"url": "https://arxiv.org/abs/solv-int/9802009"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1ba9d232-dbc9-4950-8c86-18efeb65b694",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}