Unitary representations of affine Hecke algebras related to Macdonald spherical functions
arXiv:1209.3291 · doi:10.1016/j.jalgebra.2012.01.005
Abstract
For any reduced crystallographic root system, we introduce a unitary representation of the (extended) affine Hecke algebra given by discrete difference-reflection operators acting in a Hilbert space of complex functions on the weight lattice. It is shown that the action of the center under this representation is diagonal on the basis of Macdonald spherical functions. As an application, we compute an explicit Pieri formula for these spherical functions.
arXiv comment30 pages, 1 figure
References in corpus (5)
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- Periodic integrable systems with delta-potentials
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- On the Kazhdan-Lusztig basis of a spherical Hecke algebra
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Cited by in corpus (6)
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- Discrete harmonic analysis on a Weyl alcove
- A discrete analogue of periodic delta Bose gas and affine Hecke algebra
- Affine Pieri rule for periodic Macdonald spherical functions and fusion rings