Mathematik-Bericht 2009/8 Convolution algebras for Heckman- Opdam polynomials derived from compact Grassmannians
نویسندگان
چکیده
We study convolution algebras associated with HeckmanOpdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/K with fixed rank over the real, complex or quaternionic numbers. These convolution algebras are linked to explicit positive product formulas for Heckman-Opdam polynomials of type BC, which occur for certain discrete multiplicities as the spherical functions of U/K. These results complement those of a recent paper by the second author for the noncompact case.
منابع مشابه
Convolution algebras for Heckman-Opdam polynomials derived from compact Grassmannians
We study convolution algebras associated with Heckman–Opdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/K with fixed rank over the real, complex or quaternionic numbers. These convolution algebras are linked to explicit positive produ...
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