On R-Matrix Representations of Birman--Murakami--Wenzl Algebras
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 147-153
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It is shown that, to every local representation of the Birman–Murakami–Wenzl algebra defined by a skew invertible R-matrix $\hat R\in\mathrm{Aut}(V^{\otimes 2})$, one can associate pairings $V\otimes V\rightarrow\mathbb C$ and $V^*\otimes V^*\rightarrow\mathbb C$, where $V$ is the representation space. Further, conditions are investigated under which the corresponding quantum group is of SO or Sp type.
@article{TM_2004_246_a9,
author = {A. P. Isaev and O. V. Ogievetskii and P. N. Pyatov},
title = {On {R-Matrix} {Representations} of {Birman--Murakami--Wenzl} {Algebras}},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {147--153},
publisher = {mathdoc},
volume = {246},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2004_246_a9/}
}
TY - JOUR AU - A. P. Isaev AU - O. V. Ogievetskii AU - P. N. Pyatov TI - On R-Matrix Representations of Birman--Murakami--Wenzl Algebras JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2004 SP - 147 EP - 153 VL - 246 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_2004_246_a9/ LA - ru ID - TM_2004_246_a9 ER -
%0 Journal Article %A A. P. Isaev %A O. V. Ogievetskii %A P. N. Pyatov %T On R-Matrix Representations of Birman--Murakami--Wenzl Algebras %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 2004 %P 147-153 %V 246 %I mathdoc %U http://geodesic.mathdoc.fr/item/TM_2004_246_a9/ %G ru %F TM_2004_246_a9
A. P. Isaev; O. V. Ogievetskii; P. N. Pyatov. On R-Matrix Representations of Birman--Murakami--Wenzl Algebras. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 147-153. http://geodesic.mathdoc.fr/item/TM_2004_246_a9/