9 D ec 1 99 8 Kazhdan - Lusztig conjecture for symmetrizable Kac - Moody Lie algebras . III Positive

نویسندگان

  • Mikio Sato
  • Masaki Kashiwara
چکیده

2 Highest weight modules 4 2.1 Kac-Moody Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Integral Weyl groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Category of highest weight modules . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Enright functor for non-integral weights . . . . . . . . . . . . . . . . . . . . 11 2.5 Embeddings of Verma modules . . . . . . . . . . . . . . . . . . . . . . . . 16

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

Almost split real forms for hyperbolic Kac-Moody Lie algebras

A Borel-Tits theory was developped for almost split forms of symmetrizable Kac-Moody Lie algebras [J. of Algebra 171, 43-96 (1995)]. In this paper, we look to almost split real forms for symmetrizable hyperbolic KacMoody Lie algebras and we establish a complete list of these forms, in terms of their Satake-Tits index, for the strictly hyperbolic ones and for those which are obtained as (hyperbo...

متن کامل

Automorphisms and derivations of Borel subalgebras and their nilradicals in Kac-Moody algebras

In this paper, we determine derivations of Borel subalgebras and their derived subalgebras called nilradicals, in Kac-Moody algebras (and contragredient Lie algebras) over any field of characteristic 0; and we also determine automorphisms of those subalgebras in symmetrizable Kac-Moody algebras. The results solve a conjecture posed by R. V. Moody about 30 years ago which generalizes a result by...

متن کامل

Polytopes for Crystallized Demazure Modules and Extremal Vectors

Demazure’s character formula for arbitrary Kac-Moody Lie algebra was given by S.Kumar and O.Mathieu independently ([6],[8]) by using geometric methods. In 1995, P.Littelmann gave some conjecture (partially solved by himself) about the relation between Demazure’s character formula and crystal bases [7], which was solved affirmatively by M.Kashiwara [3]. Then it gave purely algebraic proof for De...

متن کامل

A Lecture on Kac–moody Lie Algebras of the Arithmetic Type

We name an indecomposable symmetrizable generalized Cartan matrix A and the corresponding Kac–Moody Lie algebra g(A) of the arithmetic type if for any β ∈ Q with (β|β) < 0 there exist n(β) ∈ N and an imaginary root α ∈ ∆ such that n(β)β ≡ α mod Ker (.|.) on Q. Here Q is the root lattice. This generalizes ”symmetrizable hyperbolic” type of Kac and Moody. We show that generalized Cartan matrices ...

متن کامل

Categories of Modules over an Affine Kac–moody Algebra and the Kazhdan–lusztig Tensor Product

To each category C of modules of finite length over a complex simple Lie algebra g, closed under tensoring with finite dimensional modules, we associate and study a category AFF(C)κ of smooth modules (in the sense of Kazhdan and Lusztig [9]) of finite length over the corresponding affine Kac– Moody algebra in the case of central charge less than the critical level. Equivalent characterizations ...

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 1990