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- W3148045346 abstract "Inspired by the quantum McKay correspondence, we consider the classical ADE Lie theory as a quantum theory over $$mathfrak {sl}_2$$ . We introduce anti-symmetric characters for representations of quantum groups and investigate the Fourier duality to study the spectral theory. In the ADE Lie theory, there is a correspondence between the eigenvalues of the Coxeter element and the eigenvalues of the adjacency matrix. We formalize related notions and prove such a correspondence for representations of Verlinde algebras of quantum groups: this includes generalized Dynkin diagrams over any simple Lie algebra $$mathfrak {g}$$ at any level $$k$$ . This answers a recent comment of Terry Gannon on an old question posed by Victor Kac in 1994." @default.
- W3148045346 created "2021-04-13" @default.
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- W3148045346 date "2021-04-07" @default.
- W3148045346 modified "2023-09-23" @default.
- W3148045346 title "Antisymmetric Characters and Fourier Duality" @default.
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- W3148045346 doi "https://doi.org/10.1007/s00220-021-04047-5" @default.
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