which expresses the measure as an alternating sum of iterated convolutions of Heaviside measures. We also describe an algorithm based on this latter formula () that can in particular be applied to projections of coadjoint orbits (), and hence to the setting of Berenstein–Sjamaar [@berensteinsjamaar00].

Whenever a Hamiltonian group action can be quantized in a certain technical sense, Duistermaat–Heckman measures have an interpretation as the asymptotic limit of associated representation-theoretic quantities [@heckman82; @guilleminsternberg82b; @sjamaar95; @meinrenken96; @meinrenkensjamaar99; @vergne98]. In the second part of this article ( and ), we thus study the representation theory connected to the one-body quantum marginal problem; here, the relevant multiplicities include the Kronecker coefficients, which play a major role in the representation theory of the unitary and symmetric groups [@fulton97], as well as in Mulmuley and Sohoni’s geometric complexity theory approach to the P vs. NP problem in computer science [@mulmuleysohoni01; @mulmuleysohoni08; @mulmuley07; @burgisserlandsbergmaniveletal11]. It has been observed that the existence of a pure tripartite quantum state with given marginal eigenvalue spectra is equivalent to the asymptotic non-vanishing of an associated sequence of Kronecker coefficients [@christandlmitchison06; @klyachko04; @christandlharrowmitchison07], see also [@daftuarhayden04; @knutson09; @burgisserchristandlikenmeyer11; @burgisserchristandlikenmeyer11b]. For a similar connection in the context of Horn’s problem and Littlewood–Richardson 