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Abstract
Generalized double affine Hecke algebras (GDAHA) are flat deformations of the group algebras of 2-dimensional crystallographic groups associated to star-shaped simply laced affine Dynkin diagrams. In this paper, we first construct a functor that sends representations of the D4-type GDAHA to representations of the E6-type one for specialised parameters. Then, under no restrictions on the parameters, we construct embeddings of both GDAHAs of type D4 and E6 into matrix algebras over quantum cluster X-varieties, thus linking to the theory of higher Teichmüller spaces. For E6, the two explicit representations we provide over distinct quantum tori are shown to be related by quiver reductions and mutations.
Original language | English |
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Article number | 109763 |
Number of pages | 54 |
Journal | Advances in Mathematics |
Volume | 450 |
Early online date | 10 Jun 2024 |
DOIs | |
Publication status | Published - Jul 2024 |
Keywords
- Generalized double affine Hecke algebras
- Higher Teichmüller theory
- Category theory
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Extended Riemann Hilbert correspondence, quantum curves and mirror symmetry
Mazzocco, M. (Principal Investigator)
1/06/22 → 31/08/26
Project: Research