Quantum Supergroups Ii. Canonical Basis

نویسندگان

  • SEAN CLARK
  • WEIQIANG WANG
چکیده

Following Kashiwara’s algebraic approach, we construct crystal bases and canonical bases for quantum supergroups of anisotropic type and for their integrable modules.

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

Gauss Decomposition for Quantum Groups and Supergroups

The Gauss decompositions of the quantum groups, related to classical Lie groups and supergroups are considered by the elementary algebraic and R-matrix methods. The commutation relations between new basis generators (which are introduced by the decomposition) are described in some details. It is shown that the reduction of the independent generator number in the new basis to the dimension of re...

متن کامل

Dual Canonical Bases for the Quantum General Linear Supergroup

Dual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the quantum special linear supergroup Oq(SLm|n). We apply the canonical bases to study invariant subalgebras of the quantum supergroups under left and right translati...

متن کامل

Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

We introduce the quasi-Hopf superalgebras which are Z2 graded versions of Drinfeld’s quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymm...

متن کامل

2 4 Ja n 20 03 ON ALGEBRAIC SUPERGROUPS AND QUANTUM

We give the definitions of affine algebraic supervariety and affine algebraic supergroup through the functor of points and we relate them to the other definitions present in the literature. We study in detail the algebraic supergroups GL(m|n) and SL(m|n) and give explicitly the Hopf algebra structure of the algebra representing the functors of points. At the end we give also the quantization of...

متن کامل

Quantum Supergroups And Topological Invariants of Three - Manifolds

The Reshetikhin Turaeve approach to topological invariants of three manifolds is generalized to quantum supergroups. A general method for constructing three manifold invariants is developed, which requires only the study of the eigenvalues of certain central elements of the quantum supergroup in irreducible representations. To illustrate how the method works, Uq(gl(2|1)) at odd roots of unity i...

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 2014