Transvectants, modular forms, and the Heisenberg algebra.

DOI10.1006/aama.2000.0700zbMath1041.11026OpenAlexW1973329814MaRDI QIDQ5927943

Jan A. Sanders, Peter J. Olver

Publication date: 25 March 2001

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/c91853185d33c5255e6a4b0c71c3490734f00dc7

zbMATH Keywords

binary formHeisenberg algebramodular formtransvectant

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Coherent states (81R30) Holomorphic modular forms of integral weight (11F11) Applications of Lie algebras and superalgebras to integrable systems (17B80) Deformation quantization, star products (53D55)

Related Items (14)

Differential symmetry breaking operators. II: Rankin-Cohen operators for symmetric pairs ⋮ Singular projective bases and the affine Bol operator ⋮ Rankin-Cohen brackets, transvectants and covariant differential operators ⋮ The Lie theory of the Rankin-Cohen brackets and allied bi-differential operators ⋮ Rankin-Cohen brackets and representations of conformal Lie groups ⋮ On invariants and equivalence of differential operators under Lie pseudogroups actions ⋮ A geometric interpretation and explicit form for higher-order Hankel operators ⋮ Foundations of invariant theory for the down operator ⋮ Generalized transvectants and Siegel modular forms ⋮ Rankin-Cohen brackets and invariant theory ⋮ Rankin-Cohen brackets and associativity ⋮ Ternary invariant differential operators acting on spaces of weighted densities ⋮ Covariant quantization: spectral analysis versus deformation theory ⋮ Vect(S1) Action on Pseudodifferential Symbols on S1 and (Noncommutative) Hydrodynamic Type Systems

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