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Search Results: 1 - 10 of 1295 matches for " Masaki Kashiwara "
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Riemann-Hilbert correspondence for irregular holonomic D-modules
Masaki Kashiwara
Mathematics , 2015,
Abstract: This is a survey paper on the Riemann-Hilbert correspondence on (irregular) holonomic D-modules, based on the 16-th Takagi lecture (2015/11/28). In this paper, we use subanalytic sheaves, an analogous notion to the one of indsheaves.
On Level Zero Representations of Quantized Affine Algebras
Masaki Kashiwara
Mathematics , 2000,
Abstract: 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. Several properties of modules generated by extremal vectors are proved. The weights of a module generated by an extremal vector are contained in the convex hull of the Weyl group orbit of the extremalweight. The universal extremal weight module with level zero fundamental weight as an extremal weight is irreducible, and isomorphic to the affinization of an irreducible finite-dimensional module.
Realizations of Crystals
Masaki Kashiwara
Mathematics , 2002,
Abstract: We shall give various realizations of crystals. One of them is a monome realization introduced by Nakajima.
T-structures on the derived categories of D-modules and O-modules
Masaki Kashiwara
Mathematics , 2003,
Abstract: We give the description of the t-structure on the derived category of regular holonomic D-modules corresponding to the trivial t-structure on the derived category of constructible sheaves via Riemann-Hilbert correspondence. We give also the condition for a decreasing sequence of families of supports to give a t-structure on the derived category of coherent O-modules.
Level zero fundamental representations over quantized affine algebras and Demazure modules
Masaki Kashiwara
Mathematics , 2003,
Abstract: We show that the finite-dimensional fundamental module over a quantized affine algebra is isomorphic to a Demazure module of a higest weight module of level one as a module over a quantized classical universal enveloping algebra.
Biadjointness in cyclic Khovanov-Lauda-Rouquier Algebras
Masaki Kashiwara
Mathematics , 2011,
Abstract: We prove that the simple root functors E and F appearing in the categorification of irreducible highest weight modules of quantum groups via cyclotomic Khovanov-Lauda-Rouquier algebras is a biadjoint pair.
Notes on parameters of quiver Hecke algebras
Masaki Kashiwara
Mathematics , 2012,
Abstract: Varagnolo-Vasserot and Rouquier proved that, in a symmetric generalized Cartan matrix case, the simple modules over the quiver Hecke algebra with a special parameter correspond to the upper global basis. In this note we show that the simple modules over the quiver Hecke algebras with a generic parameter also correspond to the upper global basis in a symmetric generalized Cartan matrix case.
Self-dual T-structure
Masaki Kashiwara
Mathematics , 2015,
Abstract: We give a self-dual t-structure on the derived category of $\mathbb{R}$-constructible sheaves over a Noetherian regular ring by generalizing the notion of t-structure.
Self-dual T-structure
Masaki Kashiwara
Mathematics , 2015,
Abstract: We give a self-dual t-structure on the derived category of $\mathbb{R}$-constructible sheaves over a Noetherian regular ring by generalizing the notion of t-structure.
Symmetric crystals and affine Hecke algebras of type B
Naoya Enomoto,Masaki Kashiwara
Mathematics , 2006,
Abstract: The Lascoux-Leclerc-Thibon conjecture, reformulated and solved by S. Ariki, asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with the Lie algebra $gl_\infty$ or the affine Lie algebra $A^{(1)}_\ell$, and the irreducible representations correspond to the upper global bases. In this note, we formulate analogous conjectures for certain classes of irreducible representations of affine Hecke algebras of type B. We corrected typos.
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