Tensor Ideals in the Category of Tilting Modules

نویسنده

  • V. OSTRIK
چکیده

Let g be a complex finite dimensional simple Lie algebra with the root datum (Y,X, . . . ), see [Lu2]. Let Wf denote the Weyl group, R denote the root system, R+ denote the set of positive roots. Let X+ denote the set of dominant integral weights. Let h denote the Coxeter number of g. Let us fix l ∈ N, l > h. We assume that l is odd (and not divisible by 3, if g is of type G2). Let W denote the corresponding affine Weyl group. Let ρ ∈ 1 2 X denote the halfsum of positive roots. We will denote by dot (for example w · λ) the action of W (and Wf ⊂ W ) centered in (−ρ). Let q be a primitive l−th root of unity and let Uq be the quantum group with divided powers as defined in [Lu2]. Let C denote the category of finite dimensional Uq−modules of type 1 (see e.g. [APW]). In [An] H.Andersen has studied a tensor subcategory Q ⊂ C formed by tilting modules. He has introduced a tensor ideal K ⊂ Q formed by negligible tilting modules. The quotient tensor category Q/K is semisimple. For certain values of l it is tensor-equivalent to a category of integrable modules over affine Lie algebra ĝ equipped with a fusion tensor structure (see e.g. [F]). Let us recall the definition of K. Indecomposable tilting modules are numbered by their highest weights λ ∈ X+; we will denote them by Q(λ). The set of dominant weights X+ is covered by the closed alcoves numbered by W f ⊂ W — the set of shortest elements in the right cosets W/Wf . For w ∈ W f the corresponding closed alcove will be denoted by Cw. For example, the alcove Ce = C containing the zero weight is given by

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

Serre Subcategories and Local Cohomology Modules with Respect to a Pair of Ideals

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

متن کامل

Adjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.

For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of  Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of  Hom-tensor relations have been st...

متن کامل

Category O for Quantum Groups

In this paper we study the BGG-categories Oq associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Usin...

متن کامل

Annihilating Ideals and Tilting Functors

We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective functors known in the case of a simple Lie algebra.

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 1997