Nilpotent Representations of Classical Quantum Groups at Roots of Unity

نویسندگان

  • Yuuki Abe
  • Toshiki Nakashima
چکیده

Properly specializing the parameters in “Schnizer modules”, for type A,B,C and D, we get its unique primitive vector. Then we show that the module generated by the primitive vector is an irreducible highest weight module of finite dimensional classical quantum groups at roots of unity.

برای دانلود رایگان 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

Unitary Representations of Noncompact Quantum Groups at Roots of Unity

Noncompact forms of the Drinfeld–Jimbo quantum groups U q (g) with H∗ i = Hi, X i ∗ = siX ∓ i for si = ±1 are studied at roots of unity. This covers g = so(n, 2p), su(n, p), so∗(2l), sp(n, p), sp(l, R), and exceptional cases. Finite–dimensional unitary representations are found for all these forms, for even roots of unity. Their classical symmetry induced by the Frobenius–map is determined, and...

متن کامل

Inductive Construction of Nilpotent Modules of Quantum Groups at Roots of Unity

The purpose of this paper is to prove that we can construct all finite dimensional irreducible nilpotent modules of type 1 inductively by using Schnizer homomorphisms for quantum algebra at roots of unity of type An, Bn, Cn, Dn or G2.

متن کامل

A Quadratic Deformation of the Heisenberg-Weyl and Quantum Oscillator Enveloping Algebras

A new 2-parameter quadratic deformation of the quantum oscillator algebra and its 1-parameter deformed Heisenberg subalgebra are considered. An infinite dimensional Fock module representation is presented which at roots of unity contains null vectors and so is reducible to a finite dimensional representation. The cyclic, nilpotent and unitary representations are discussed. Witten’s deformation ...

متن کامل

Roots of Unity: Representations of Quantum Groups

Representations of Quantum Groups Uε(gn), gn any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n − 1 quantum groups for ε a root of unity. Representations which have the maximal dimension and number of free parameters for irreducible representations arise as special cases.

متن کامل

Braid Group Representations from Twisted Quantum Doubles of Finite Groups

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite groups, in contrast to the categories associated with quantum groups at roots of unity. We also show that in the case of p-groups, the corresponding pure br...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004