Yang’s system of particles and Hecke algebras. (English) Zbl 0873.43007

Heckman, G. J.; Opdam, E. M.

Ann. Math. (2) 145, No. 1, 139-173 (1997); erratum ibid. 146, 749-750 (1997).

From the summary of the authors: “The graded Hecke algebra has a simple realization as a certain algebra of operators acting on a space of smooth functions. This operator algebra arises from the study of the system analogue of Yang’s system of \(n\) particles on the real line with delta function potential. It turns out that the spectral problem for the generalization of Yang’s system is related to the problem of finding the spherical tempered representations of the graded Hecke algebra. This observation turns out to be very useful for both these problems. Application of our technique to affine Hecke algebras yields a simple formula for the formal degree of the generic Iwahori spherical discrete series representations”.

Reviewer: E.Płonka (Wodzisław)

MSC:

43A85	Harmonic analysis on homogeneous spaces
22E50	Representations of Lie and linear algebraic groups over local fields
22E35	Analysis on \(p\)-adic Lie groups

Keywords:

hypergeometric functions; Hecke algebra; operators; Yang’s system; representations