Đề tài " Invariant measures and arithmetic quantum unique ergodicity " doc

... are done. Annals of Mathematics Invariant measures and arithmetic quantum unique ergodicity By Elon Lindenstrauss INVARIANT MEASURES AND ARITHMETIC QUE 183 Proposition 4.3. Let ... Mathematics, 163 (2006), 165–219 Invariant measures and arithmetic quantum unique ergodicity By Elon Lindenstrauss* Appendix with D. Rudolph Abstract We classify me...

Ngày tải lên: 29/03/2014, 07:20

... EINSIEDLER, ANATOLE KATOK, AND ELON LINDENSTRAUSS (1) The conditional measures µ ab x and µ ba x are trivial a.e. (2) The conditional measures µ ab x and µ ba x are Haar a.e., and µ is invariant under left ... both µ ab x and µ ij x are nontrivial a.s., for distinct pairs of indices i, j and a, b with either i = a or j = b, then both µ ab x and µ ba x are in fact Haar mea...

Ngày tải lên: 15/03/2014, 09:20

... C[z, z −1 ] be its loop algebra, and U q (Lg) be its quantum universal enveloping algebra, or the quantum loop algebra for short. It is a subquotient of the quantum *Supported by the Grant-in-aid ... χ ε,t (M(Q p )) is uniquely determined by the above discussion. Therefore χ ε,t (M(P )) is also uniquely determined. (5) It is enough to check the case V = M(P ). In this case, τ ∗ a (M...

Ngày tải lên: 28/03/2014, 22:20

... Singer, and J. Weitsman, Some comments on Chern-Simons gauge theory, Comm. Math. Phys. 126 (1989), 409–420. [RT1] N. Reshetikhin and V. Turaev, Ribbon graphs and their invariants derived from quantum ... Universitet, Aarhus, Denmark E-mail address : andersen@imf.au.dk URL: http://home.imf.au.dk.andersen/ References [A1] J. E. Andersen, Jones-Witten theory and the Thurston boundary o...

Ngày tải lên: 16/02/2014, 05:20

... k-subset, and α ∈ S.Onone hand, the number of pairs in question is kf k (Φ). On the other hand, combining Proposition 2.5 and Theorem 2.6, formula (3.1), and Proposition 3.5 (Parts 1 and 3), we ... transformations τ + and τ − are involutions and preserve Φ ≥−1 . (2) τ ± (α)=t ± (α) for any α ∈ Q + . (3) The bijection α → α ∨ between Φ ≥−1 and Φ ∨ ≥−1 is τ ± -equivariant. Y-SYST...

Ngày tải lên: 05/03/2014, 23:20

... functions h 1 (˜x 1 ) and h 2 (˜x 2 ), and the right-hand side becomes −2π ∞  N=1 1 N!  − z 2π  N  T on {1, ,N}   ij∈T dΩ(y ij )ρ(h 1 )ρ(h 2 ),(5.8) where ρ(h)=  h(x j ) and the integral is ... Suppl. 69 (1980), 14–29. [Fr¨o76] J. Fr ¨ ohlich, Classical and quantum statistical mechanics in one and two dimensions: Two-component Yukawa and Coulomb systems, Comm. Math. 47 (1...

Ngày tải lên: 05/03/2014, 23:20

... Mathematics Holomorphic disks and topological invariants for closed three-manifolds By Peter Ozsv´ath and Zolt´an Szab´o HOLOMORPHIC DISKS AND THREE-MANIFOLD INVARIANTS 1045 connecting the ... T α , and u({0}×R) ⊂ T β , which are asymptotic to x and y as t →− and +∞, in the following sense. There is a real number T>0 and sections ξ − ∈ L p 1,δ  [0, 1] × (−∞, −T...

Ngày tải lên: 05/03/2014, 23:20

... Holomorphic disks and three- manifold invariants: Properties and applications By Peter Ozsv´ath and Zolt´an Szab´o* HOLOMORPHIC DISKS AND THREE-MANIFOLD INVARIANTS 1177 4. Comparison ... n z r (φ)=0for r<i− 2, and n z r (φ)=1for r ≥ i − 2. Also, n z r (ψ)=1for r ≤ i − 2, and n z r (ψ)=0for r>i− 2. Proof. We draw the domains D(φ) and D(ψ) belonging to φ and...

Ngày tải lên: 05/03/2014, 23:20

... lim k→∞ H q k (z)=H q (z). (b) Let  ≥ 1 and let q be a primitive  th root of unity, and (2.10) ρ(q k ) > 2 −2/ ,k≥ 1. Let Ω 1 and Ω 2 be open connected sets with Ω 1 ⊆ Ω 2 and Ω 1 containing a branchpoint ... G q (z) and G q (βqz). The zeros of G q (βqz) need not be poles of H q , and yet (2.16) shows that they attract poles of the convergents. Moreover as the zeros of H q a...

Ngày tải lên: 22/03/2014, 15:21

... inequality is invariant under M¨obius transformations, we may assume that C is a wedge, with one vertex at 0 and the other at infinity. Then D and D  become euclidean halfplanes and Ω contains ... Sullivan– Thurston [27], Bers–Royden [3], and Slodkowski [25]. The strongest of these is Slodkowski’s and that has been further expanded to an equivariant form in [14] and, independentl...

Ngày tải lên: 22/03/2014, 16:20