Abstract
We construct the basic representation of the double affine Hecke algebra at critical level q = 1 associated to an irreducible reduced affine root system R with a reduced gradient root system. For R of untwisted type such a representation was studied by Oblomkov [A. Oblomkov, Double affine Hecke algebras and Calogero-Moser spaces, Represent. Theory 8 (2004) 243-266] and further detailed by Gehles [K. E. Gehles, Properties of Cherednik algebras and graded Hecke algebras, PhD thesis, University of Glasgow (2006)] in the presence of minuscule weights.
Original language | English |
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Article number | 2450061 |
Number of pages | 1 |
Journal | Journal of Algebra and its Applications |
Volume | 23 (2024) |
Issue number | 3 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Affine Hecke algebras
- affine Lie algebras
- representation theory
- root systems