Generalized double affine Hecke algebras, their representations, and higher Teichmüller theory

Davide Dal Martello*, Marta Mazzocco

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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 languageEnglish
Article number109763
Number of pages54
JournalAdvances in Mathematics
Volume450
Early online date10 Jun 2024
DOIs
Publication statusPublished - Jul 2024

Keywords

  • Generalized double affine Hecke algebras
  • Higher Teichmüller theory
  • Category theory

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