Geodesic
Representations of quantum conjugacy classes of orthosymplectic groups
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 20-40

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Let $G$ be the complex symplectic or special orthogonal group and $\mathfrak g$ its Lie algebra. With every point $x$ of the maximal torus $T\subset G$ we associate a highest weight module $M_x$ over the Drinfeld–Jimbo quantum group $U_q(\mathfrak g)$ and a quantization of the conjugacy class of $x$ by operators in $\mathrm{End}(M_x)$. These quantizations are isomorphic for $x$ lying on the same orbit of the Weyl group, and $M_x$ support different representations of the same quantum conjugacy class. 
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     author = {Th. Ashton and A. Mudrov},
     title = {Representations of quantum conjugacy classes of orthosymplectic groups},
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     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a1/}
}
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Th. Ashton; A. Mudrov. Representations of quantum conjugacy classes of orthosymplectic groups. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 20-40. http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a1/