ar X iv : f un ct - a n / 96 12 00 2 v 1 1 7 D ec 1 99 6 ITERATED FUNCTION SYSTEMS AND PERMUTATION REPRESENTATIONS OF THE CUNTZ ALGEBRA
نویسنده
چکیده
We study a class of representations of the Cuntz algebras O N , N = 2, 3,. .. , acting on L 2 (T) where T = R2πZ. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show how the O N-irreducibles decompose when restricted to the subalgebra UHF N ⊂ O N of gauge-invariant elements; and we show that the whole structure is accounted for by arithmetic and combinatorial properties of the integers Z. We have general results on a class of representations of O N on Hilbert space H such that the generators S i as operators permute the elements in some orthonormal basis for H. We then use this to extend our results from L 2 (T) to L 2 T d , d > 1; even to L 2 (T) where T is some fractal version of the torus which carries more of the algebraic information encoded in our representations.
منابع مشابه
ar X iv : 0 81 1 . 00 21 v 2 [ he p - th ] 1 7 N ov 2 00 8 ITP
N=4 superconformaln-particle quantum mechanics on the real line is governed by two prepotentials, U andF , which obey a system of partial nonlinear differential equations generalizing the Witten-DijkgraafVerlinde-Verlinde (WDVV) equation for F . The solutions are encoded by the finite Coxeter systems and certain deformations thereof, which can be encoded by particular polytopes. We provide An a...
متن کاملPrimitive partial permutation representations of the polycyclic monoids and branching function systems
We characterise the maximal proper closed inverse submonoids of the polycyclic inverse monoids, also known as Cuntz inverse semigroups, and so determine all their primitive partial permutation representations. We relate our results to the work of Kawamura on certain kinds of representations of the Cuntz C∗-algebras and to the branching function systems of Bratteli and Jorgensen.
متن کامل1 N ov 1 99 9 BIASES IN THE SHANKS – RÉNYI PRIME NUMBERS RACE
Rubinstein and Sarnak investigated systems of inequalities of the form π(x; q, a 1) > · · · > π(x; q, a r), where π(x; q, a) denotes the number of primes up to x that are congruent to a mod q. They showed, under standard hypotheses on the zeros of Dirichlet L-functions mod q, that the set of positive real numbers x for which these inequalities hold has positive (logarithmic) density δ q;a 1 ,.....
متن کاملN=4 Mechanics, Wdvv Equations and Polytopes
N=4 superconformaln-particle quantum mechanics on the real line is governed by two prepotentials, U andF , which obey a system of partial nonlinear differential equations generalizing the Witten-DijkgraafVerlinde-Verlinde (WDVV) equation for F . The solutions are encoded by the finite Coxeter systems and certain deformations thereof, which can be encoded by particular polytopes. We provide An a...
متن کاملPseudo Cuntz Algebra and Recursive FP Ghost System in String Theory
Representation of the algebra of FP (anti)ghosts in string theory is studied by generalizing the recursive fermion system in the Cuntz algebra constructed previously. For that purpose, the pseudo Cuntz algebra, which is a ∗-algebra generalizing the Cuntz algebra and acting on indefinite-metric vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory is embedded into the pse...
متن کامل