Explicit construction of Rankin-Cohen-type differential operators for vector-valued Siegel modular forms (Q2772942)

A Rankin-Cohen type operator is a differential operator which associates a modular form to a pair of modular forms, and such operators have been studied for various types of modular forms. Let \((\rho, V)\) be an irreducible representation of the group GL\((n,\mathbb C)\) on a complex vector space \(V\). In this paper the author constructs a Rankin-Cohen type operator which maps Siegel modular forms \(f_1\) and \(f_2\) of weights \(\ell_1\) and \(\ell_2\), respectively, to a \(V\)-valued Siegel modular form of weight \(\det^{\ell_1+\ell_2} \otimes \rho\).