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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. Isaeva, A. I. Molevb

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
References:
Abstract: It is shown that all primitive idempotents for the Brauer algebra $\mathcal B_n(\omega)$ can be found by evaluating a rational function in several variables that has the form of a product of $R$-matrix type factors. This provides an analog of the fusion procedure for $\mathcal B_n(\omega)$.
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:
    1. 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)  crossref
    2. Alexey Silantyev, “Manin matrices of type C: Multi-parametric deformation”, Journal of Geometry and Physics, 177 (2022), 104523  crossref
    3. Alexey Silantyev, “Manin Matrices for Quadratic Algebras”, SIGMA, 17 (2021), 066, 81 pp.  mathnet  crossref
    4. Isaev A.P., Karakhanyan D., Kirschner R., “Yang-Baxter R-Operators For Osp Superalgebras”, Nucl. Phys. B, 965 (2021), 115355  crossref  mathscinet  isi
    5. 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  crossref  mathscinet  isi
    6. Bulgakova V D., Ogievetsky O., “Fusion Procedure For the Walled Brauer Algebra”, J. Geom. Phys., 149 (2020), 103580  crossref  mathscinet  isi
    7. Gerrard A., Regelskis V., “Nested Algebraic Bethe Ansatz For Orthogonal and Symplectic Open Spin Chains”, Nucl. Phys. B, 952 (2020), 114909  crossref  mathscinet  isi
    8. 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  crossref  mathscinet  isi
    9. 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  crossref  mathscinet  isi  scopus
    10. Cui W., “Fusion Procedure For Cyclotomic Bmw Algebras”, Algebr. Represent. Theory, 21:3 (2018), 565–578  crossref  mathscinet  zmath  isi  scopus
    11. King O.H., Martin P.P., Parker A.E., “On Central Idempotents in the Brauer Algebra”, J. Algebra, 512 (2018), 20–46  crossref  mathscinet  zmath  isi  scopus
    12. Cui W., “Fusion Procedure For Yokonuma-Hecke Algebras”, Colloq. Math., 154:1 (2018), 31–45  crossref  mathscinet  zmath  isi  scopus
    13. 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  crossref  mathscinet  zmath  isi  scopus
    14. d'Andecy L.P., “Fusion Formulas and Fusion Procedure For the Yang–Baxter Equation”, Algebr. Represent. Theory, 20:6 (2017), 1379–1414  crossref  mathscinet  zmath  isi  scopus
    15. Zhao D., Li Ya., “Fusion Procedure For Degenerate Cyclotomic Hecke Algebras”, Algebr. Represent. Theory, 18:2 (2015), 449–461  crossref  mathscinet  zmath  isi  elib  scopus
    16. 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  crossref  mathscinet  zmath  isi  elib  scopus
    17. d'Andecy L.P., “Fusion Procedure For Wreath Products of Finite Groups By the Symmetric Group”, Algebr. Represent. Theory, 17:3 (2014), 809–830  crossref  mathscinet  zmath  isi  scopus
    18. 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  crossref  mathscinet  zmath  isi  elib  scopus
    19. Molev A.I., “Feigin–Frenkel center in types B, C and DD”, Invent. Math., 191:1 (2013), 1–34  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    20. Molev A.I., Rozhkovskaya N., “Characteristic Maps for the Brauer Algebra”, J. Algebr. Comb., 38:1 (2013), 15–35  crossref  mathscinet  zmath  isi  scopus
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    Алгебра и анализ St. Petersburg Mathematical Journal
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