A Haar component for quantum limits on locally symmetric spaces
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...
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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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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2012
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-012-0133-x