I discuss a construction of explicit natural covariant differential operators that are the projections to the irreducible summand in hte branching laws when we restrict irreducible representations to subgroups (or subalgebras). In particular, I propose a new method (F-method) to produce naturally Juhl's differential operators in conformal geometry and the Cohen-Rankin operators in holomorphic automorphic forms. If time permits, I will also discuss some new progress on the underlying representation theoretic theory.Reference:

T. Kobayashi.F-method for constructing equivariant differential operators. Comtemporary Mathematics 598, pages 141-148. Amer. Math. Soc., 2013

T. Kobayashi.Restrictions of generalized Verma modules to symmetric pairs. Transformation Groups 17, (2012), 523-546.

T. Kobayashi,F-method for continuous restriction operators, preprint, 20 pp. arXiv:1303.3541.

T. Kobayashi, B. Ørsted, P. Somberg, V. Souček, preprint.

T. Kobayashi and M. Pevzner,Rankin-Cohen operators for symmetric pairs, preprint, arXiv:1301.2111.

© Toshiyuki Kobayashi