We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. Asâ€¦ (More)

2. Let X be a smooth complex manifold and Y a smooth submanifold of X. We denote by 0 X and ~y the sheaf of holomorphic functions on X and the defining Ideal of Y. We denote by A the gradedâ€¦ (More)

A decomposition of the level-one q-deformed Fock representations of U q (b sl n) is given. It is found that the action of U 0 q (b sl n) on these Fock spaces is centralized by a Heisenberg algebra,â€¦ (More)

We study the properties of level zero modules over quantized affine algebras. The proof of the conjecture on the cyclicity of tensor products by Akasaka and the present author is given. Severalâ€¦ (More)

In this paper we shall study the restriction of holonomic systems of differential equations. Let X be a complex manifold and Y a submanifold, and let (9 x and D x be the sheaf of the holomorphicâ€¦ (More)

We give the description of the t-structure on the derived category of regular holonomic D-modules corresponding to the trivial tstructure on the derived category of constructible sheaves via Riemannâ€“â€¦ (More)

Our motivation is to study the geometric theory of Weyl group representations, so called Springer's representations (see [21] and its references), from the view point of holonomic systems on Lieâ€¦ (More)

We shall give a description of the intersection cohomology groups of the Schubert varieties in partial flag manifolds over symmetrizable Kac-Moody Lie algebras in terms of parabolic Kazhdan-Lusztigâ€¦ (More)