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On representations of quantum conjugacy classes of GL(n) | | Thomas Ashton
; Andrey Mudrov
; | | Date: |
26 Apr 2013 | | Abstract: | Let $O$ be a closed Poisson conjugacy class of the complex algebraic Poisson
group GL(n) relative to the Drinfeld-Jimbo factorizable classical r-matrix.
Denote by $T$ the maximal torus of diagonal matrices in GL(n). With every $ain
Ocap T$ we associate a highest weight module $M_a$ over the quantum group
$U_q(gl(n))$ and an equivariant quantization $C_{h,a}[O]$ of the polynomial
ring $C[O]$ realized by operators on $M_a$. All quantizations $C_{h,a}[O]$ are
isomorphic and can be regarded as different exact representations of the same
algebra, $C_{h}[O]$. Similar results are obtained for semisimple adjoint orbits
in $gl(n)$ equipped with the canonical GL(n)-invariant Poisson structure. | | Source: | arXiv, 1304.7106 | | Services: | Forum | Review | PDF | Favorites | |
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