A representation of an arbitrary sheaf from derived category of sheaves on a stack G/G (action by conjugacy) in terms of "dual" basis. Abelian case — Fourier-Mukai transform for abelian varieties which relates sheaves on A with sheaves on Av using the correspondence A\times Av.

(there's some important property of Fourier missing above — I'll return to this tomorrow). It's something about relationship between G/G and G^\wedge/G^\wedge.

After passing to functions, you may think about the resulting version as rewriting an arbitrary conjugate-invariant function as a sum by characters. That specializes to abelian case — where all functions are conjugate-invariant.

As an example, for the real line you have to present f(x) as an integral of e^{2\lambda ix} (well, L^2, i and the appearance of integral are some important technical details because of non-compactness). The correspondence after all becomes integration with the kernel K(x, \lambda) = e^{2\lambda ix}.

A representation of an arbitrary sheaf from derived category of sheaves on a stack G/G (action by conjugacy) in terms of some "dual" basis(e.g. . Abelian case Fourier-Mukai transform for abelian varieties which relates sheaves on A and with sheaves on Av).

(there's some important property of Fourier missing above — I'll return to this tomorrow)tomorrow). It's something about relationship between G/G and G^\wedge/G^\wedge.

After passing to functions, you may think about the resulting version as rewriting an arbitrary conjugate-invariant function as a sum by characters. That specializes to abelian case — where all functions are conjugate-invariant.

As an example, for the real line you have to present f(x) as an integral of e^{2\lambda ix} (well, L^2, i and the appearance of integral are some important technical details because of non-compactness).

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A representation of an arbitrary sheaf from derived category of sheaves on a stack G/G (action by conjugacy) in terms of some basis sheaves (e.g. Fourier-Mukai transform for abelian varieties)varieties which relates A and Av).

(there's some important property of Fourier missing above I'll return to this tomorrow)

After passing to functions, you may think about the resulting version as rewriting an arbitrary conjugate-invariant function as a sum by characters. That specializes to abelian case — where all functions are conjugate-invariant.

As an example, for the real line you have to present f(x) in the basis as an integral of e^{2\lambda ix} (well, L^2, i and the appearance of integral are some important technical details because of non-compactness).

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