Kyoto University · 수학
마시키 카시와라 교수의 연구실은 주로 대수기하학, 미분방정식 이론, 양자군 및 양자 대수의 표현 이론을 중심으로 한 기하적 표현 이론을 연구합니다. 특히, 미분 연산자와 위상수학적 구조의 관계를 다루는 D-모듈 기반의 해석기하학, 큼직한 기하학적 구조(예: 쿠이버 다양체)를 통한 양자군의 스칼라 표현 기하화, 그리고 특이점 이론과 관련된 코homology 이론의 유한성 문제를 다룹니다. 이는 현대 수학의 핵심 분야인 기하 양자화와 표현 이론의 깊이 있는 통찰을 제공합니다.
표시된 성과는 수집된 데이터 기준으로 산출되며, 일부 차이가 있을 수 있습니다.
This result was announced in [K]. Mebkout [Me] gave another proof to this theorem. 0. 2. In [KK], we have already shown that J x gives an equivalence and that DR X is fully faithful; i.e. for any Jt\ -^"' e Dj h ( ^x) > we have 0.3. (Sflf-^dim X], and *:D b (X)->D b (X) by x Here o denotes the opposite category and Q x denotes the sheaf of differential forms with the highest degree. Then we have DR X * = *DR X and **=id. 0. 4. Now for ^'eD? h (^z) 5 we put F'=DR X W)*. Then in [KK] we have prove
We study the properties of level-zero modules over quantized affine algebras. The proof of the conjecture on the cyclicity of tensor products by T. Akasaka and the 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 extremal weight. The universal extremal weight module with level-zero fundamental weight as an extremal weight is irreducible,
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. As a by-product, we give a counterexample to the conjecture of Kazhdan-Lusztig on the irreducibility of the characteristic variety of the intersection cohomology sheaves associated with the Schubert cells of type A and also to the similar problem asked by Lusztig on the characteristic variety of the pe
The first one is [6] and the second one is [8].(*#) g (resp., J^) denotes the sheaf of micro-differential (resp.linear differential) operators of finite order.See also the list of notations given at the end of this section.Example.Let us consider the following ordinary differential equation:If a 7*0, (0.1) is clearly an equation with irregular singularities.Now consider the following correspondences (0.2) and (0.3).CO 00© (^m/^m-i) is Noetherian.It is easy to verify that © (^m/^m-i) is a m=0 m=0
