Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Is there a well-defined non-holomorphic index-raising operator $V_l$, taking index-$m$ Jacobi-Maass forms to index-$ml$ Jacobi-Maass forms (same weight), analogous to the holomorphic operator defined in Eichler-Zagier, p.41? I haven't found it in the literature yet.

share|improve this question
add comment

1 Answer 1

It may well be that no explicit expressions have been written down for the corresponding operator for Jacobi-Maass forms, but the analogous operators surely exist and behave reasonably, for the following reason(s). The Eichler-Zagier operator (and Maass-Shimura operators, in other contexts) are in-coordinates expressions for differential operators coming from the enveloping algebra of the Lie algebra, regardless of the weight/index and/or holomorphy/waveform features, which would refer to the (irreducible or not) representation in which we are "moving around". That is, the intrinsic prescription of the operators (as opposed to the formulaic/in-coordinates description) does not depend on the holomorphy-or-waveform feature, nor upon the index and/or weight. Yes, the expressions for the operators certainly depend, but this is in principle a secondary issue.

Thus, one can be reassured that it is possible to obtain the desired operators, and be assured in advance that they have the expected/desired properties.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.