Berezin-Karpelevich formula for chi-spherical functions on complex Grassmannians

Authors

  • Mahmoud Al-Hashami Sultan Qaboos University

Keywords:

Spherical Functions, Hermitian Symmetric Spaces, Jacobi Function, Laplace-Beltrami Operator

Abstract

In [5], Berezin and Karpelevich gave, without a proof, an explicit formula for spherical functions on complex Grassmannian manifolds. A first attempt to give a proof of Berezin-Karpelevich formula was taken, in [16], by Takahashi. His proof contained a gap, which was fixed later, in [10], by Hoogenboom. The aim of this paper is to generalize Berezin-Karpelevich formula to the case of $\chi$-spherical functions on complex Grassmannian manifolds $ SU(p+q)/S\left(U(p)\times U(q)\right)$.

Author Biography

Mahmoud Al-Hashami, Sultan Qaboos University

Department of Mathematics
Sultan Qaboos University
Alkhoud
Sultanate of Oman

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Published

2020-11-14

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Section

Articles