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.
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
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Linking options:
https://www.mathnet.ru/eng/aa1189
https://www.mathnet.ru/eng/aa/v22/i3/p142
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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