Remarks on Diffeological Frobenius Reciprocity
Symplectic Geometry
2026-02-12 v3 Representation Theory
Abstract
A recent paper [R22] established "Frobenius reciprocity" as a bijection between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1{\deg}) is a diffeomorphism when these spaces are endowed with their natural subquotient diffeologies, 2{\deg}) respects the reduced diffeological -forms they may (or might not) carry. In this paper, we prove both this conjecture and a similar one on prequantum reduction, and also give new sufficient conditions for the reduced forms to exist. We stop short of proving that they always exist.
Cite
@article{arxiv.2403.03927,
title = {Remarks on Diffeological Frobenius Reciprocity},
author = {Gabriele Barbieri and Jordan Watts and Francois Ziegler},
journal= {arXiv preprint arXiv:2403.03927},
year = {2026}
}
Comments
v3 to appear in Trans. AMS: added table row (5.7h) and reference [H19], both inadvertently omitted from v2