Abstract
We introduce families \( \mathcal{B}_n^S\left( {{z_1},\ldots,{z_n}} \right) \) and \( \mathcal{B}_{{n,\hbar}}^S\left( {{z_1},\ldots,{z_n}} \right) \) of maximal commutative subalgebras, called Bethe subalgebras, of the group algebra \( \mathbb{C}\left[ {\mathfrak{S}n} \right] \) of the symmetric group. Bethe subalgebras are deformations of the Gelfand−Zetlin subalgebra of \( \mathbb{C}\left[ {\mathfrak{S}n} \right] \). We describe various properties of Bethe subalgebras.
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*Supported in part by NSF grant DMS-0900984.
**Supported in part by NSF grant DMS-0901616.
***Supported in part by NSF grant DMS-0555327.
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Mukhin*, E., Tarasov**, V. & Varchenko**, A. Bethe subalgebras of the group algebra of the symmetric group. Transformation Groups 18, 767–801 (2013). https://doi.org/10.1007/s00031-013-9232-y
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DOI: https://doi.org/10.1007/s00031-013-9232-y