On the basic representation of the double affine Hecke algebra at critical level
J. F. Van Diejen (University of Talca)
E. Emsiz (TU Delft - Electrical Engineering, Mathematics and Computer Science)
I. N. Zurrián (University of Seville)
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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.