A. P. Isaev, A. I. Molev, “Fusion procedure for the Brauer algebra”, Algebra i Analiz, 22:3 (2010), 142–154; St. Petersburg Math. J., 22:3 (2011), 437

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Algebra i Analiz, 2010, Volume 22, Issue 3, Pages 142–154 (Mi aa1189)

This article is cited in 23 scientific papers (total in 23 papers)

Research Papers

Fusion procedure for the Brauer algebra

A. P. Isaev^a, A. I. Molev^b

^a Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow region, Russia
^b School of Mathematics and Statistics, University of Sydney, Australia

Full-text PDF (621 kB) Citations (23)

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Abstract: It is shown that all primitive idempotents for the Brauer algebra

B_{n} (ω)

$\mathcal B_n(\omega)$ can be found by evaluating a rational function in several variables that has the form of a product of

R

$R$ -matrix type factors. This provides an analog of the fusion procedure for

B_{n} (ω)

$\mathcal B_n(\omega)$ .

Keywords: fusion procedure, Brauer algebra, up-down tableau, Young tableau.

Received: 15.01.2010

English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 3, Pages 437–446
DOI: https://doi.org/10.1090/S1061-0022-2011-01150-1

Bibliographic databases:

Document Type: Article

Language: English

Citation: A. P. Isaev, A. I. Molev, “Fusion procedure for the Brauer algebra”, Algebra i Analiz, 22:3 (2010), 142–154; St. Petersburg Math. J., 22:3 (2011), 437–446

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/aa1189

https://www.mathnet.ru/eng/aa/v22/i3/p142

This publication is cited in the following 23 articles:

S. E. Derkachov, A. P. Isaev, L. A. Shumilov, “Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles”, J. High Energ. Phys., 2023:6 (2023)
Alexey Silantyev, “Manin matrices of type C: Multi-parametric deformation”, Journal of Geometry and Physics, 177 (2022), 104523
Alexey Silantyev, “Manin Matrices for Quadratic Algebras”, SIGMA, 17 (2021), 066, 81 pp.
Isaev A.P., Karakhanyan D., Kirschner R., “Yang-Baxter R-Operators For Osp Superalgebras”, Nucl. Phys. B, 965 (2021), 115355
Isaev A.P., Podoinitsyn M.A., “D-Dimensional Spin Projection Operators For Arbitrary Type of Symmetry Via Brauer Algebra Idempotents”, J. Phys. A-Math. Theor., 53:39 (2020), 395202
Bulgakova V D., Ogievetsky O., “Fusion Procedure For the Walled Brauer Algebra”, J. Geom. Phys., 149 (2020), 103580
Gerrard A., Regelskis V., “Nested Algebraic Bethe Ansatz For Orthogonal and Symplectic Open Spin Chains”, Nucl. Phys. B, 952 (2020), 114909
Podoinitsyn M.A., “Polarization Spin-Tensors in Two-Spinor Formalism and Behrends-Fronsdal Spin Projection Operator For D-Dimensional Case”, Phys. Part. Nuclei Lett., 16:4 (2019), 315–320
Butorac M., Jing N., Kozic S., “H-Adic Quantum Vertex Algebras Associated With Rational R-Matrix in Types B, C and D”, Lett. Math. Phys., 109:11 (2019), 2439–2471
Cui W., “Fusion Procedure For Cyclotomic Bmw Algebras”, Algebr. Represent. Theory, 21:3 (2018), 565–578
King O.H., Martin P.P., Parker A.E., “On Central Idempotents in the Brauer Algebra”, J. Algebra, 512 (2018), 20–46
Cui W., “Fusion Procedure For Yokonuma-Hecke Algebras”, Colloq. Math., 154:1 (2018), 31–45
Fuksa J., Isaev A.P., Karakhanyan D., Kirschner R., “Yangians and Yang–Baxter R-operators for ortho-symplectic superalgebras”, Nucl. Phys. B, 917 (2017), 44–85
d'Andecy L.P., “Fusion Formulas and Fusion Procedure For the Yang–Baxter Equation”, Algebr. Represent. Theory, 20:6 (2017), 1379–1414
Zhao D., Li Ya., “Fusion Procedure For Degenerate Cyclotomic Hecke Algebras”, Algebr. Represent. Theory, 18:2 (2015), 449–461
Ogievetsky O.V., D'Andecy L.P., “Fusion Procedure For Coxeter Groups of Type B and Complex Reflection Groups $G(m,1,n)$”, Proc. Amer. Math. Soc., 142:9 (2014), 2929–2941
d'Andecy L.P., “Fusion Procedure For Wreath Products of Finite Groups By the Symmetric Group”, Algebr. Represent. Theory, 17:3 (2014), 809–830
Isaev A.P., Molev A.I., Ogievetsky O.V., “Idempotents For Birman-Murakami-Wenzl Algebras and Reflection Equation”, Adv. Theor. Math. Phys., 18:1 (2014), 1–25
Molev A.I., “Feigin–Frenkel center in types B, C and DD”, Invent. Math., 191:1 (2013), 1–34
Molev A.I., Rozhkovskaya N., “Characteristic Maps for the Brauer Algebra”, J. Algebr. Comb., 38:1 (2013), 15–35

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

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