Double affine Hecke algebra

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위키데이터

• ID : Q5299963

말뭉치

1. An infinite-dimensional representation of the double affine Hecke algebra of rank 1 and type \((C_1^{\vee },C_1)\) in which all generators are tridiagonal is presented.
2. We classify the finite dimensional irreducible representations of the double affine Hecke algebra (DAHA) of type C ∨ C 1 in the case when q is not a root of unity.
3. Well the first thing to say is to look at the very enthusiastic and world-encompassing papers of Cherednik himself on DAHA as the center of the mathematical world (say his 1998 ICM).
4. There are at least three distinct geometric appearances of DAHA, which you could classify by the number of loops (as in loop groups) that appear - two, one or zero.
5. The idea here is that DAHA appears as the K-group of coherent sheaves on G(O)\G(K)/G(O) - the loop group version of the Bruhat cells in the finite flag manifold (again ignoring Borels vs parabolics).
6. The Cherednik Fourier transform gives an identification between DAHA for G and the dual group G'.
7. We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators.
8. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras.
9. We prove the existence of an involution on double affine Hecke algebras.
10. My naive and general question is: if it really does not exist, why infinite dimensional, non polynomial representations of DAHA/Askey-Wilson have not been considered?
11. We formulate a conjecture which interprets DAHA superpolynomials colored by fundamental weights to the Borel-Moore cohomology of Jacobian factors and their flagged and higher rank generalizations.
12. We focus on an algebra embedding from the rational Cherednik algebra to the degenerate DAHA and investigate the induction functor through this embedding.

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위키데이터

• ID : Q5299963