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Local Systems on P1 - S for S a Finite Set
  • P. Belkale
  • Mathematics
  • Compositio Mathematica
  • 1 October 2001
I give the necessary and sufficient conditions for the existence of Unitary local systems with prescribed local monodromies on P1 − S where S is a finite set. This is used to give an algorithm toExpand
Geometric proofs of horn and saturation conjectures
We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of HornExpand
Eigenvalue problem and a new product in cohomology of flag varieties
Let G be a connected semisimple complex algebraic group and let P be a parabolic subgroup. In this paper we define a new (commutative and associative) product on the cohomology of the homogenousExpand
Matroids motives, and a conjecture of Kontsevich
Let G be a finite connected graph. The Kirchhoff polynomial of G is a certain homogeneous polynomial whose degree is equal to the first betti number of G. These polynomials appear in the study ofExpand
On finite generation of the section ring of the determinant of cohomology line bundle
For $C$ a stable curve of arithmetic genus $g\ge 2$, and $\mathcal{D}$ the determinant of cohomology line bundle on $\operatorname{Bun}_{\operatorname{SL}(r)}(C)$, we show the section ring for theExpand
Quantum generalization of the Horn conjecture
(Recall that the Lie algebra of the special unitary group SU(n) is isomorphic to the real vector space of traceless Hermitian matrices as representations of SU(n) and hence the terminology "additiveExpand
The strange duality conjecture for generic curves
Let SUX(r) be the moduli space of semi-stable vector bundles of rank r with trivial determinant over a connected smooth projective algebraic curve X of genus g ≥ 1 over C. Recall that a vector bundleExpand
Periods and Igusa local zeta functions
We show that the coefficients in the Laurent series of the Igusa local zeta functions I(s) = ∫ C fω are periods. This is proved by first showing the existence of functional equations for theseExpand
Strange duality and the Hitchin/WZW connection
For a compact Riemann surface X of positive genus, the space of sections of certain theta bundle on moduli of bundles of rank r and level k admits a natural map to (the dual of) a similar space ofExpand
In this paper we consider the eigenvalue problem, intersection theory of homogeneous spaces (in particular, the Horn problem) and the saturation problem for the symplectic and odd orthogonal groups.Expand