TY - GEN
T1 - Remarks on Diffeological Frobenius Reciprocity
AU - Barbieri, G.
AU - Watts, J.
AU - Ziegler, F.
PY - 2025
Y1 - 2025
N2 - A recent paper [R22] established "Frobenius reciprocity" as a bijection between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1°) is a diffeomorphism when these spaces are endowed with their natural subquotient diffeologies, 2°) 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.
AB - A recent paper [R22] established "Frobenius reciprocity" as a bijection between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1°) is a diffeomorphism when these spaces are endowed with their natural subquotient diffeologies, 2°) 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.
UR - https://www.scopus.com/inward/record.url?eid=2-s2.0-85188652868&partnerID=MN8TOARS
U2 - 10.48550/arXiv.2403.03927
DO - 10.48550/arXiv.2403.03927
M3 - Other
ER -