Weight Changing Operators for Automorphic Forms on Grassmannians and Differential Properties of Certain Theta Lifts

Abstract

We define weight changing operators for automorphic forms on Grassmannians, i.e., on orthogonal groups, and investigate their basic properties. We then evaluate their action on theta kernels, and prove that theta lifts of modular forms, in which the theta kernel involves polynomials of a special type, have some interesting differential properties.

30 pages, changed the name because the previous main theorem is substantially simplified, and added more results

References in corpus (2)

• A Gross--Kohnen--Zagier Type Theorem for Higher-Codimensional Heegner Cycles
• A $p$-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices

Cited by in corpus (3)

• The Structure of Integral Parabolic Subgroups of Orthogonal Groups
• Orthogonal Eisenstein Series at Harmonic Points and Modular Forms of Singular Weight
• Jacobi Forms of Indefinite Lattice Index