Cremmer-Gervais r-matrices and the Cherednik Algebras of type GL2

Details Cremmer-Gervais r-matrices and the Cherednik Algebras of type GL2 Cremmer-Gervais r-matrices and the Cherednik Algebras of type GL2

2009-10-28

arxiv.org/abs/0910.5505v1

Mathematics

Quantum Algebra

6 pages

Scientific paper

We give an intepretation of the Cremmer-Gervais r-matrices for sl(n) in terms of actions of elements in the rational and trigonometric Cherednik algebras of type GL2 on certain subspaces of their polynomial representations. This is used to compute the nilpotency index of the Jordanian r-matrices, thus answering a question of Gerstenhaber and Giaquinto. We also give an interpretation of the Cremmer-Gervais quantization in terms of the corresponding double affine Hecke algebra.

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