Motivic interpretation of genus 2 Siegel forms induced by lifts of Maass and Skoruppa - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T18:19:21Z http://mathoverflow.net/feeds/question/72209 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72209/motivic-interpretation-of-genus-2-siegel-forms-induced-by-lifts-of-maass-and-skor Motivic interpretation of genus 2 Siegel forms induced by lifts of Maass and Skoruppa Laie 2011-08-05T21:00:21Z 2011-08-06T20:08:54Z <p><strong>Background:</strong> There are several known lifts from integral weight modular forms to Siegel forms of genus 2, among them the Saito-Kurokawa lift. Another lift construction that is important for applications combines the Maass lift, which maps Jacobi forms to Siegel forms, with a lift of Skoruppa, which maps forms of integral weight $w$ with respect to ${\rm SL}(2,{\mathbb Z})$ to Jacobi forms of weight $(w-2)$. An example of this construction is the lift of the weight 12 form $\Delta(\tau) = \eta(\tau)^{24}$ to the Igusa form of weight 10. Thinking about motives in the context of Siegel forms of genus 2 leads to the following two questions.</p> <p><strong>Question 1:</strong> Has the lift construction by Maass and Skoruppa been generalized in a systematic way to congruence subgroups, for example $\Gamma_0(N)$?</p> <p><strong>Question 2:</strong> Is there a motivic interpretation of this lift by Maass and Skoruppa?</p> <p>(Some references: the work of Skoruppa is in his 1992 paper (Math. of Comp. 58); a partial generalization of Skoruppa's lift to congruence subgroups has been considered by Gritsenko and collaborators in several papers. The Maass lift has been extended to restricted levels $N>1$ by Manickam-Ramakrishnan-Vasudevan in a 1993 paper (manuscripta math. 81). Question 1 is asking whether more systematic extensions are known.)</p>