dorsal/arxiv
View SchemaFinite dimensional unitary representations of quantum Anti-de Sitter groups at roots of unity
| Authors | Harold Steinacker |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9611009 |
| URL | https://arxiv.org/abs/q-alg/9611009 |
| DOI | 10.1007/s002200050315 |
| Journal | Commun.Math.Phys. 192 (1998) 687-706 |
Abstract
We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are found for $q = e^{i \pi /M}$, with $M$ being large enough. In the "massless" case with spin bigger than or equal to 1 in 4 dimensions, they are unitarizable only after factoring out a subspace of "pure gauges", as classically. A truncated associative tensor product describing unitary many-particle representations is defined for $q = e^{i\pi /M}$.
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"abstract": "We study irreducible unitary \\reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for\n$q$ a root of unity, which are finite dimensional. Among others, unitary \\reps\ncorresponding to all classical one-particle representations with integral\nweights are found for $q = e^{i \\pi /M}$, with $M$ being large enough. In the\n\"massless\" case with spin bigger than or equal to 1 in 4 dimensions, they are\nunitarizable only after factoring out a subspace of \"pure gauges\", as\nclassically. A truncated associative tensor product describing unitary\nmany-particle representations is defined for $q = e^{i\\pi /M}$.",
"arxiv_id": "q-alg/9611009",
"authors": [
"Harold Steinacker"
],
"categories": [
"q-alg",
"hep-th",
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],
"doi": "10.1007/s002200050315",
"journal_ref": "Commun.Math.Phys. 192 (1998) 687-706",
"title": "Finite dimensional unitary representations of quantum Anti-de Sitter groups at roots of unity",
"url": "https://arxiv.org/abs/q-alg/9611009"
},
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