D. R. Karakhanyan, “Realization of the Universal $s\ell_q(2)$-Symmetric $R$-Operator in a Function Space for General and Exceptional Values of the Deformation Parameter”, TMF, 135:2 (2003), 196–223; Theoret. and Math. Phys., 135:2 (2003), 614

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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 135, Number 2, Pages 196–223
DOI: https://doi.org/10.4213/tmf182 (Mi tmf182)

This article is cited in 2 scientific papers (total in 2 papers)

Realization of the Universal

s ℓ_{q} (2)

$s\ell_q(2)$ -Symmetric

R

$R$ -Operator in a Function Space for General and Exceptional Values of the Deformation Parameter

D. R. Karakhanyan

Yerevan Physics Institute

Full-text PDF (323 kB) Citations (2)

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DOI: https://doi.org/10.4213/tmf182

Abstract: Based on the realization of representations of the algebra

s ℓ_{q} (2)

$s\ell_q(2)$ in the space of polynomials for general values of the deformation parameter

q

$q$ and on a finite tuple of theta functions, which are a natural generalization of polynomials, we construct the eigenstates and find the related eigenvalues of the universal

R

$R$ -operator for cyclic representations corresponding to

q^{N} = \pm 1

$q^N=\pm1$ .

Keywords: exactly solvable models, universal

R

$R$ -matrix, cyclic representations,

N

$N$ th root of unity, eigenvalues.

Received: 13.05.2002

English version:
Theoretical and Mathematical Physics, 2003, Volume 135, Issue 2, Pages 614–637
DOI: https://doi.org/10.1023/A:1023662330333

Bibliographic databases:

Language: Russian

Citation: D. R. Karakhanyan, “Realization of the Universal

s ℓ_{q} (2)

$s\ell_q(2)$ -Symmetric

R

$R$ -Operator in a Function Space for General and Exceptional Values of the Deformation Parameter”, TMF, 135:2 (2003), 196–223; Theoret. and Math. Phys., 135:2 (2003), 614–637

Citation in format AMSBIB

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\by D.~R.~Karakhanyan

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\transl

\jour Theoret. and Math. Phys.

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\issue 2

\pages 614--637

\crossref{https://doi.org/10.1023/A:1023662330333}

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Linking options:

https://www.mathnet.ru/eng/tmf182

https://doi.org/10.4213/tmf182

https://www.mathnet.ru/eng/tmf/v135/i2/p196

This publication is cited in the following 2 articles:

Karakhanyan, D, “Fusion rules of the lowest weight representations of osp(q)(1 vertical bar 2) at roots of unity: polynomial realization”, Journal of Physics A-Mathematical and Theoretical, 42:37 (2009), 375205
Karakhanyan D, Khachatryan S, “Polynomial realization of sl(q)(2) and fusion rules at exceptional values of q”, Letters in Mathematical Physics, 72:2 (2005), 83–97

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	48
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