Geodesic
Root vectors in quantum groups
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 212-234

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We propose a definition of root vectors in a finite dimensional quantum group which are compatible with the adjoint action of every quantum Levi subgroup (deliver highest and lowest vectors of finite dimensional submodules). We assign for that role certain entries of reduced quantum Lax matrices associated with the fundamental adjoint module of the quantum group. This study is motivated by the theory of Mickelsson algebras. 
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     author = {N. V. Kryazhevskikh and A. I. Mudrov},
     title = {Root vectors in quantum groups},
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     publisher = {mathdoc},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a9/}
}
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N. V. Kryazhevskikh; A. I. Mudrov. Root vectors in quantum groups. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 212-234. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a9/