Construction à la Ibukiyama of Symmetry Breaking Differential Operators

J. Math. Sci. Univ. Tokyo
Vol. 29 (2022), No. 1, Page 51-88.

Clerc, Jean-Louis
Construction à la Ibukiyama of Symmetry Breaking Differential Operators
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]


Abstract:
The construction of symmetry breaking differential operators, using invariant pluriharmonic polynomials, due to T. Ibukiyama in the context of the Siegel upper half space, is extended for scalar representations to general Hermitian symmetric spaces of tube-type. The new context is described in terms of Euclidean Jordan algebras and their representations. As an example, new and explicit differential operators are obtained for the restriction from the tube domain over the light cone to the product of two upper half-planes.

Keywords: tube-type domain, Euclidean Jordan algebra, holomorphic representations, pluriharmonic polynomial, symmetry breaking differential operator.

Mathematics Subject Classification (2010): Primary 32M15; Secondary 17C20, 22E46, 11F70.
Mathematical Reviews Number: MR4414247

Received: 2021-04-16