Unimodularity and atomic Plancherel measure

1984 ◽  
Vol 266 (4) ◽  
pp. 513-518 ◽  
Author(s):  
L. Baggett
Keyword(s):  
Plancherel Measure

The Plancherel measure for p-forms in real hyperbolic spaces

1994 ◽  
Vol 15 (1) ◽  
pp. 57-94 ◽  
Author(s):  
Roberto Camporesi ◽  
Atsushi Higuchi
Keyword(s):  
Hyperbolic Spaces ◽  
Plancherel Measure

On Limit Multiplicities for Spaces of Automorphic Forms

1999 ◽  
Vol 51 (5) ◽  
pp. 952-976 ◽  
Author(s):  
Anton Deitmar ◽  
Werner Hoffmann
Keyword(s):  
Lie Group ◽  
Automorphic Forms ◽  
Plancherel Measure ◽  
Semisimple Lie Group ◽  
Selberg Trace Formula ◽  
Arithmetic Subgroup ◽  
Trivial Group ◽  
Rank One ◽  
Discrete Part ◽  
Cocompact Lattices

AbstractLet Γ be a rank-one arithmetic subgroup of a semisimple Lie group G. For fixed K-Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of G, whose discrete part encodes the dimensions of the spaces of square-integrable Γ-automorphic forms. It is shown that this distribution converges to the Plancherel measure of G when Γ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices Γ follows from results of DeGeorge-Wallach and Delorme.

Tensor Square of the Minimal Representation of O(p, q)

2007 ◽  
Vol 50 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Alexander Dvorsky
Keyword(s):  
Tensor Product ◽  
Hyperbolic Space ◽  
Irreducible Representations ◽  
Plancherel Measure ◽  
Minimal Representation ◽  
Direct Integral ◽  
Tensor Square ◽  
Real Hyperbolic Space

AbstractIn this paper, we study the tensor product π = σmin ⊗ σmin of the minimal representation σmin of O(p, q) with itself, and decompose π into a direct integral of irreducible representations. The decomposition is given in terms of the Plancherel measure on a certain real hyperbolic space.

scholarly journals Gaussian fluctuations of Young diagrams under the Plancherel measure

2007 ◽  
Vol 463 (2080) ◽  
pp. 1069-1080 ◽  
Author(s):  
Leonid V Bogachev ◽  
Zhonggen Su
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Gaussian Process ◽  
Central Limit ◽  
Point Processes ◽  
Plancherel Measure ◽  
Young Diagrams ◽  
Finite Dimensional ◽  
The Central Limit Theorem ◽  
Local Correlations

We obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the ‘spectrum’ of partitions λ ⊢ n ∈ (under the Plancherel measure), thus settling a long-standing problem posed by Logan & Shepp. Namely, under normalization growing like , the corresponding random process in the bulk is shown to converge, in the sense of finite-dimensional distributions, to a Gaussian process with independent values, while local correlations in the vicinity of each point, measured on various power scales, possess certain self-similarity. The proofs are based on the Poissonization techniques and use Costin–Lebowitz–Soshnikov's central limit theorem for determinantal random point processes. Our results admit a striking reformulation after the rotation of Young diagrams by 45°, whereby the normalization no longer depends on the location in the spectrum. In addition, we explain heuristically the link with an earlier result by Kerov on the convergence to a generalized Gaussian process.

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