Integral exotic sheaves and the modular Lusztig–Vogan bijection

Modular sheaves and representations

Perverse sheaves and modular representation theory

This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and nilpotent cones to modular representations of reductive groups and their Weyl groups. The second part is a brief introduction to the theory of perverse shea...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Simulating Perverse Sheaves in Modular Representation Theory

For some time we have studied the representation theory of semisimple algebraic groups in characteristic p > 0. Of special interest is a celebrated conjecture of Lusztig [Ll] describing the characters of the simple modules when p is not too small relative to the root system. A similar conjecture, by Kazhdan and Lusztig [KLl], for the composition factor multiplicities of Verma modules for semisi...

Integral modular data and congruences

We compute all fusion algebras with symmetric rational S-matrix up to dimension 12. Only two of them may be used as S-matrices in a modular datum: the S-matrices of the quantum doubles of Z/2Z and S3. Almost all of them satisfy a certain congruence which has some interesting implications, for example for their degrees. We also give explicitly an infinite sequence of modular data with rational S...