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Francois Ziegler
Francois Ziegler
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Some niceNice examples are worked out in Audin (2004, §VI.3.d), Arvanitoyeorgos (1999)  (pdf), McDuff-Salamon (1998, §5.6). It’s not true that $\omega$ is rarely explicit: e.g. on all coadjoint orbits (including your $\smash{S^2}$ example) it is is, and DH gives a formula of Harish-Chandra for their Fourier transforms; see Berline-Vergne (1983), Vergne (1983), or Guillemin-Sternberg (1984, ends of §§33 and 34).

Some nice examples are worked out in Audin (2004, §VI.3.d), Arvanitoyeorgos (1999)  (pdf), McDuff-Salamon (1998, §5.6). It’s not true that $\omega$ is rarely explicit: e.g. on all coadjoint orbits (including your $\smash{S^2}$ example) it is, and DH gives a formula of Harish-Chandra for their Fourier transforms; see Berline-Vergne (1983) or Guillemin-Sternberg (1984, ends of §§33 and 34).

Nice examples are worked out in Audin (2004, §VI.3.d), Arvanitoyeorgos (1999)(pdf), McDuff-Salamon (1998, §5.6). It’s not true that $\omega$ is rarely explicit: e.g. on all coadjoint orbits (including $\smash{S^2}$) it is, and DH gives a formula of Harish-Chandra for their Fourier transforms; see Berline-Vergne (1983), Vergne (1983), or Guillemin-Sternberg (1984, ends of §§33 and 34).

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Francois Ziegler
Francois Ziegler
  • 31.5k
  • 6
  • 121
  • 176

Some nice examples are worked out in Audin (2004, §VI.3.d), Arvanitoyeorgos (1999) (pdf), McDuff-Salamon (1998, §5.6). It’s not true that $\omega$ is rarely explicit: e.g. on all coadjoint orbits (including your $\smash{S^2}$ example) it is, and DH gives a formula of Harish-Chandra for their Fourier transforms; see Berline-Vergne (1983) or Guillemin-Sternberg (1984, ends of §§33 and 34).