6 research outputs found
Harish-Chandra integrals as nilpotent integrals
Recently the correlation functions of the so-called
Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors
and collaborators) for all classical groups using an integration formula that
relates integrals over compact groups with respect to the Haar measure and
Gaussian integrals over a maximal nilpotent Lie subalgebra of their
complexification. Since the integration formula a posteriori had the same form
for the classical series, a conjecture was formulated that such a formula
should hold for arbitrary semisimple Lie groups. We prove this conjecture using
an abstract Lie-theoretic approach.Comment: 10 page
A matrix model for the topological string II: The spectral curve and mirror geometry
In a previous paper, we presented a matrix model reproducing the topological
string partition function on an arbitrary given toric Calabi-Yau manifold.
Here, we study the spectral curve of our matrix model and thus derive, upon
imposing certain minimality assumptions on the spectral curve, the large volume
limit of the BKMP "remodeling the B-model" conjecture, the claim that
Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the
spectral invariants of its mirror curve.Comment: 1+37 page