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arXiv · 2403.03927

Remarks on Diffeological Frobenius Reciprocity

Gabriele Barbieri·Jordan Watts·Francois Ziegler
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Abstract

A recent paper [R22] established "Frobenius reciprocity" as a bijection $t$ between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1{\deg}) $t$ is a diffeomorphism when these spaces are endowed with their natural subquotient diffeologies, 2{\deg}) $t$ respects the reduced diffeological $2$-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.

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Gabriele Barbieri, Jordan Watts, Francois Ziegler. 2024-03-06. Remarks on Diffeological Frobenius Reciprocity. https://doi.org/10.1090/tran%2F9565

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