Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift
نویسندگان
چکیده
منابع مشابه
On Quantum Unique Ergodicity for Locally Symmetric Spaces I
We construct an equivariant microlocal lift for locally symmetric spaces. In other words, we demonstrate how to lift, in a “semicanonical” fashion, limits of eigenfunction measures on locally symmetric spaces to Cartan-invariant measures on an appropriate bundle. The construction uses elementary features of the representation theory of semisimple real Lie groups, and can be considered a general...
متن کاملQuantum Unique Ergodicity for Locally Symmetric Spaces Ii
We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for non-degenerate sequences of Hecke eigenfunctions on quotients Γ\G/K, where G ' PGLd(R), K is a maximal compact subgroup of G and Γ < G is a lattice associated to a division algebra over Q of prime degree d. The primary novelty of the present paper is a new method of proving positive entropy of quantum limits, which avoids s...
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We construct an equivariant microlocal lift for locally symmetric spaces. In other words, we demonstrate how to lift, in a “semicanonical” fashion, limits of eigenfunction measures on locally symmetric spaces to Cartan-invariant measures on an appropriate bundle. The construction uses elementary features of the representation theory of semisimple real Lie groups, and can be considered a general...
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The purpose of this note is to record an observation about quantum unique ergodicity (QUE) which is relevant to the recent construction of H. Donnelly [D] of quasi-modes on nonpositively curved surfaces and to similar examples known as bouncing ball modes [BSS, H] on stadia. It gives a rigorous proof of a localization statement of Heller-O’Connor [HO] for eigenfunctions of the stadium. The rele...
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In this work we prove that every locally symmetric smooth submanifoldM of Rn gives rise to a naturally defined smooth submanifold of the space of n × n symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs toM. We also present an explicit formula for the dimension of the spectral manifold in terms of the dimension and the intrinsic ...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2015
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2015-023-0