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Vector partition functions, difference equations, and indices of transversally elliptic operators

Michele Vergne
Analysis Seminar
Thursday, 6 May, 2010, at 16:15, in Aud. D3 (1531-215)

Consider a complex vector space with a linear action of a torus $T$. We will show that the equivariant $K$-theory of the open set $U$ where orbits have maximal dimension is equivalent to a space of functions on the lattice $\hat T$ satisfying difference equations. I will start with the case of the space $C^n$ with rotation $e^{i\theta}$: the binomial coefficients, and Pascal triangle will show up naturally.

Then I will show that indices of any elliptic or transversally elliptic operators are linear combinations of partition functions.

Contact person: Bent Ørsted