6j SYMBOLS FOR Uq(sl2) AND NON-EUCLIDEAN TETRAHEDRA
نویسندگان
چکیده
We relate the semiclassical asymptotics of the 6j symbols for the quantized enveloping algebra Uq(sl2) at q a root of unity (resp. q real positive) to the geometry of spherical (resp. hyperbolic) tetrahedra.
منابع مشابه
Uq(sl2) AND NON-EUCLIDEAN TETRAHEDRA
In this paper we study the semiclassical asymptotics of the 6j symbols for the representation theory of the quantized enveloping algebra Uq(sl2) for q a primitive root of unity. Because of the work of Finkelberg [7], these 6j symbols can also be defined in terms of fusion product of representations of the affine Lie algebra ŝl2, defined using Wess-Zumino-Witten conformal field theory. This asso...
متن کاملFerromagnetic Ordering of Energy Levels for Uq(sl2) Symmetric Spin Chains
We consider the class of quantum spin chains with arbitrary Uq(sl2)-invariant nearest neighbor interactions, sometimes called SUq(2) for the quantum deformation of SU(2), for q > 0. We derive sufficient conditions for the Hamiltonian to satisfy the property we call Ferromagnetic Ordering of Energy Levels. This is the property that the ground state energy restricted to a fixed total spin subspac...
متن کاملON REPRESENTATIONS OF QUANTUM GROUPS Uq(f(K, H)) To Prof. Yingbo Zhang on the occasion of her 60th birthday
As further generalizations of Uq(sl2), an interesting class of algebras Uq(f(K,H)) was introduced and studied in [10]. In this paper, we further study these algebras by realizing them as Hyperbolic algebras. Such a realization yields a natural construction of interesting families of irreducible representations of Uq(f(K,H)) by using methods in non-commutative algebraic geometry([16]). We also i...
متن کاملMapping Class Group Actions on Quantum Doubles
We study representations of the mapping class group of the punctured torus on the double of a finite dimensional possibly non-semisimple Hopf algebra that arise in the construction of universal, extended topological field theories. We discuss how for doubles the degeneracy problem of TQFT’s is circumvented. We find compact formulae for the S±1-matrices using the canonical, non degenerate forms ...
متن کاملQUANTUM BASES IN Uq(g)
This paper is devoted to analyze, inside the ∞-many possible bases of a Quantum Universal Enveloping Algebra Uq(g), those that can be considered as “more equal then others”, like orthonormal bases in the Euclidean spaces. The only possible element of selection has been found to be a privileged connection with the corresponding bialgebra. A new parameter z ∈ C –independent from the z := log(q) ∈...
متن کامل