F-method for constructing equivariant differential operators

Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that arise in parabolic geometry and in automorphic forms.

[1]  V. Souček,et al.  Branching laws for Verma modules and applications in parabolic geometry. I , 2013, 1305.6040.

[2]  Toshiyuki Kobayashi,et al.  RANKIN-COHEN OPERATORS FOR SYMMETRIC PAIRS , 2013 .

[3]  Toshiyuki Kobayashi,et al.  Differential symmetry breaking operators. I-Genreal theory and F-method. II-Rankin-Cohen Operators for Symmetric Pairs , 2013, 1301.2111.

[4]  Toshiyuki Kobayashi.  Restrictions of generalized Verma modules to symmetric pairs , 2010, 1008.4544.

[5]  A. Juhl.  Families of Conformally Covariant Differential Operators, Q-Curvature and Holography , 2009 .

[6]  Toshiyuki Kobayashi,et al.  The Schrödinger model for the minimal representation of the indefinite orthogonal group ( , 2007, 0712.1769.

[7]  Toshiyuki Kobayashi.  Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs , 2006, math/0607002.

[8]  Toshiyuki Kobayashi.  Visible actions on symmetric spaces , 2006, math/0607005.

[9]  G. Dijk,et al.  Ring structures for holomorphic discrete series and Rankin-Cohen brackets , 2005, math/0512096.

[10]  R. Rankin,et al.  The Construction of Automorphic Forms From the Derivatives of a Given Form II , 1985, Canadian Mathematical Bulletin.

[11]  Henri Cohen,et al.  Sums involving the values at negative integers of L-functions of quadratic characters , 1975 .

[12]  小林 俊行,et al.  The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p, q) , 2011 .

[13]  Paula B. Cohen,et al.  AUTOMORPHIC PSEUDODIFFERENTIAL OPERATORS , 1997 .