Asymptotics of quantum $6j$ symbols
نویسندگان
چکیده
The asymptotics of the quantum $6j$ symbols corresponding to a hyperbolic tetrahedron is investigated and first two leading terms are determined for case that has an ideal or ultra-ideal vertex. These given by volume determinant Gram matrix tetrahedron.
منابع مشابه
Asymptotics and 6j-symbols
Recent interest in the Kashaev-Murakami-Murakami hyperbolic volume conjecture has made it seem important to be able to understand the asymptotic behaviour of certain special functions arising from representation theory — for example, of the quantum 6j -symbols for SU(2). In 1998 I worked out the asymptotic behaviour of the classical 6j -symbols, proving a formula involving the geometry of a Euc...
متن کاملQuantum Teichmüller spaces and Kashaev’s 6j –symbols
The Kashaev invariants of 3–manifolds are based on 6j –symbols from the representation theory of the Weyl algebra, a Hopf algebra corresponding to the Borel subalgebra of Uq.sl.2;C// . In this paper, we show that Kashaev’s 6j –symbols are intertwining operators of local representations of quantum Teichmüller spaces. This relates Kashaev’s work with the theory of quantum Teichmüller space, which...
متن کامل6j –symbols, hyperbolic structures and the volume
We compute the asymptotical growth rate of a large family of Uq.sl2/ 6j –symbols and we interpret our results in geometric terms by relating them to volumes of hyperbolic truncated tetrahedra. We address a question which is strictly related with S Gukov’s generalized volume conjecture and deals with the case of hyperbolic links in connected sums of S S . We answer this question for the infinite...
متن کاملCLASSICAL 6j-SYMBOLS AND THE TETRAHEDRON
A classical 6j-symbol is a real number which can be associated to a labelling of the six edges of a tetrahedron by irreducible representations of SU(2). This abstract association is traditionally used simply to express the symmetry of the 6j-symbol, which is a purely algebraic object; however, it has a deeper geometric significance. Ponzano and Regge, expanding on work of Wigner, gave a strikin...
متن کاملAN ELEMENTARY APPROACH TO 6j-SYMBOLS (CLASSICAL, QUANTUM, RATIONAL, TRIGONOMETRIC, AND ELLIPTIC)
Elliptic 6j-symbols first appeared in connection with solvable models of statistical mechanics. They include many interesting limit cases, such as quantum 6j-symbols (or q-Racah polynomials) and Wilson’s biorthogonal 10W9 functions. We give an elementary construction of elliptic 6j-symbols, which immediately implies several of their main properties. As a consequence, we obtain a new algebraic i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2023
ISSN: ['1945-743X', '0022-040X']
DOI: https://doi.org/10.4310/jdg/1679503803