Geodesic
On interaction of symplectic and orthogonal Hecke--Shimura rings of one-class quadratic forms
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 5-17

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Transformation formulas of theta-series with harmonic polynomials of one-class quadratic forms under Hecke operators are interpreted as a result of interaction of standard representation of symplectic Hecke–Shimura ring on theta-series with natural representation of orthogonal Hecke–Shimura ring on the same theta-series considered as invariants of quadratic forms. Properties of the interaction maps and their relations with action of Hecke operators are considered. 
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     author = {A. N. Andrianov},
     title = {On interaction of symplectic and orthogonal {Hecke--Shimura} rings of one-class quadratic forms},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a0/}
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A. N. Andrianov. On interaction of symplectic and orthogonal Hecke--Shimura rings of one-class quadratic forms. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a0/