dorsal/arxiv
View SchemaHighest weight irreducible representations of the quantum algebra $U_h(A_\infty)$
| Authors | T. D. Palev, N. I. Stoilova |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709004 |
| URL | https://arxiv.org/abs/q-alg/9709004 |
| DOI | 10.1063/1.532597 |
Abstract
A class of highest weight irreducible representations of the algebra $U_h(A_\infty)$, the quantum analogue of the completion and central extension $A_\infty$ of the Lie algebra $gl_\infty$, is constructed. It is considerably larger than the known so far representations. Within each module a basis is introduced and the transformation relations of the basis under the action of the Chevalley generators are explicitly written. The verification of the quantum algebra relations to be satisfied is shown to reduce to a set of nontrivial $q$-number identities. All our representations are restricted in the terminology of S. Levendorskii and Y. Soibelman (Commun. Math. Phys. 140, 399-414 (1991)).
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"abstract": "A class of highest weight irreducible representations of the algebra\n$U_h(A_\\infty)$, the quantum analogue of the completion and central extension\n$A_\\infty$ of the Lie algebra $gl_\\infty$, is constructed. It is considerably\nlarger than the known so far representations. Within each module a basis is\nintroduced and the transformation relations of the basis under the action of\nthe Chevalley generators are explicitly written. The verification of the\nquantum algebra relations to be satisfied is shown to reduce to a set of\nnontrivial $q$-number identities. All our representations are restricted in the\nterminology of S. Levendorskii and Y. Soibelman (Commun. Math. Phys. 140,\n399-414 (1991)).",
"arxiv_id": "q-alg/9709004",
"authors": [
"T. D. Palev",
"N. I. Stoilova"
],
"categories": [
"q-alg",
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"math.QA"
],
"doi": "10.1063/1.532597",
"title": "Highest weight irreducible representations of the quantum algebra $U_h(A_\\infty)$",
"url": "https://arxiv.org/abs/q-alg/9709004"
},
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