منابع مشابه
Quantum Racah Coefficients and Subrepresentation Semirings
Let G be a group and A a G-algebra. The subrepresentation semiring of A is the set of subrepresentations of A endowed with operations induced by the algebra operations. The introduction of these semirings was motivated by a problem in material science. Typically, physical properties of composite materials are strongly dependent on microstructure. However, in exceptional situations, exact relati...
متن کاملWilson Function Transforms Related to Racah Coefficients
The irreducible ∗-representations of the Lie algebra su(1, 1) consist of discrete series representations, principal unitary series and complementary series. We calculate Racah coefficients for tensor product representations that consist of at least two discrete series representations. We use the explicit expressions for the Clebsch-Gordan coefficients as hypergeometric functions to find explici...
متن کاملHolography for the Lorentz Group Racah Coefficients
A known realisation of the Lorentz group Racah coefficients is given by an integral of a product of 6 “propagators” over 4 copies of the hyperbolic space. These are “bulk-to-bulk” propagators in that they are functions of two points in the hyperbolic space. It is known that the bulk-to-bulk propagator can be constructed out of two bulk-to-boundary ones. We point out that there is another way to...
متن کاملRacah Coefficients, Subrepresentation Semirings, and Composite Materials
Typically, physical properties of composite materials are strongly dependent on the microstructure. However, in exceptional situations, there exists exact formulas for the effective properties of composites which are microstructure-independent. These formulas represent fundamental physical invariances. The classical approach to exact relations suffered from the drawback that the methods used we...
متن کاملA Simple Class of U ( N ) Racah Coefficients and Their Application
Using permutation group techniques, a genera1 expression is derived for the special class of U(N) Racah coefficients for which the representations [fl] and [f3] in the recoupling matrix for [fl] x [f2] x [f3]-~[f] are either both totally antisymmetric or both totally symmetric. For the totally antisymmetric case further specialization gives a simple expression for a U(N) Racah coefficient which...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1966
ISSN: 0025-5718
DOI: 10.2307/2003516