A Mackey Decomposition Theorem and Cohomology for Quantum Groups at Roots of 1

نویسنده

  • Zongzhu Lin
چکیده

Introduction This is a continuation of the investigation in [L3] into the module structure of those modules for quantum enveloping algebras U analogous to the coho-mology groups of line bundles on the flag varieties for semisimple algebraic groups. In [L3], we used the admissible categories for Hopf algebras and their induction theory and proved a modified Borel-Bott-Weil theorem for R l(w) Ind

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

متن کامل

George Mackey and His Work on Representation Theory and Foundations of Physics

This article is a retrospective view of the work of George Mackey and its impact on the mathematics of his time and ours. The principal themes of his work–systems of imprimitivity, induced representations, projective representations, Borel cohomology, metaplectic representations, and so on, are examined and shown to have been central in the development of the theory of unitary representations o...

متن کامل

De Rham Cohomology and Hodge Decomposition for Quantum Groups

ISTVÁN HECKENBERGER and AXEL SCHÜLER Abstra t Let Γ = Γτ,z be one of the N -dimensional bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or Spq(N), where q is a transcendental complex number and z is a regular parameter. It is shown that the de Rham cohomology of Woronowicz’ external algebra Γ coincides with the de Rham cohomologies of its left-coinvar...

متن کامل

Two Classifications of Simple Mackey Functors with Applications to Group Cohomology and the Decomposition of Classifying Spaces

In previous joint work with Thévenaz we have classified simple Mackey functors [15] and developed a structural theory of Mackey functors which takes its standpoint from representation theory [16]. In this paper we show that this type of theory may be used to perform specific calculations of Mackey functor values, and also to obtain structural results about the decomposition of classifying space...

متن کامل

Quantum Groups at Roots of Unity and Modularity

For each compact, simple, simply-connected Lie group and each integer level we construct a modular tensor category from a quotient of a certain subcategory of the category of representations of the corresponding quantum group. We determine when at fractional levels the corresponding category is modular. We also give a quantum version of the Racah formula for the decomposition of the tensor prod...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1993