18 citations · 21 across the 5 of their papers we have counts for
6 papers
Generalized double affine Hecke algebras of higher rank
Pavel Etingof, Wee Liang Gan, Alexei Oblomkov
We define generalized double affine Hecke algebras (GDAHA) of higher rank, attached to a non-Dynkin star-like graph D. This generalizes GDAHA of rank 1 defined in math.QA/0406480 a…
Generalized double affine Hecke algebras of rank 1 and quantized Del Pezzo surfaces
Pavel Etingof, Alexei Oblomkov, Eric Rains
Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators corresp…
Laplace transformations and spectral theory of two-dimensional semi-discrete and discrete hyperbolic Schroedinger operators
Alexei A. Oblomkov, Alexei V. Penskoi
We introduce Laplace transformations of 2D semi-discrete hyperbolic Schroedinger operators and show their relation to a semi-discrete 2D Toda lattice. We develop the algebro-geomet…
Quantization, orbifold cohomology, and Cherednik algebras
Pavel Etingof, Alexei Oblomkov
We compute the Hochschild homology of the crossed product in terms of the Hochschild homology of the associative algebra (over ). It…
Double affine Hecke algebras of rank 1 and affine cubic surfaces
Alexei Oblomkov
We study the algebraic properties of the five-parameter family of double affine Hecke algebras of type . This family generalizes Cherednik's doub…
Jack polynomials for the root system and generalized spherical functions
Alexei Oblomkov
We give a construction for three parameter family of Jack polynolials for the root system through the generalized spherical functions on the symmetric space $GL(m+n)/GL(m)\t…