Explicit Plancherel Measure for $\mathrm{PGL}_2(\mathbb{F})$
نویسندگان
چکیده
منابع مشابه
PLANCHEREL MEASURE FOR GL(n): EXPLICIT FORMULAS AND BERNSTEIN DECOMPOSITION
Let F be a nonarchimedean local field, let GL(n) = GL(n, F ) and let ν denote Plancherel measure for GL(n). Let Ω be a component in the Bernstein variety Ω(GL(n)). Then Ω yields its fundamental invariants: the cardinality q of the residue field of F , the sizes m1, . . . ,mt, exponents e1, . . . , et, torsion numbers r1, . . . , rt, formal degrees d1, . . . , dt and the Artin conductors f11, . ...
متن کاملStein's Method and Plancherel Measure of the Symmetric Group Running Head: Stein's Method and Plancherel Measure
X iv :m at h/ 03 05 42 3v 3 [ m at h. R T ] 1 1 N ov 2 00 3 Stein’s Method and Plancherel Measure of the Symmetric Group Running head: Stein’s Method and Plancherel Measure By Jason Fulman University of Pittsburgh Department of Mathematics 301 Thackeray Hall Pittsburgh, PA 15260 Email: [email protected] Abstract: We initiate a Stein’s method approach to the study of the Plancherel measure of...
متن کاملCentral Limit Theorem for Random Partitions under the Plancherel Measure
A partition of a natural number n is any integer sequence λ = (λ1, λ2, . . . ) such that λ1 ≥ λ2 ≥ · · · ≥ 0 and λ1 + λ2 + · · · = n (notation: λ ⊢ n). In particular, λ1 = max{λi ∈ λ}. Every partition λ ⊢ n can be represented geometrically by a planar shape called the Young diagram, consisting of n unit cell arranged in consecutive columns, containing λ1, λ2, . . . cells, respectively. On the s...
متن کاملReiter P2–condition and the Plancherel Measure for Hypergroups
In this paper we study the Reiter P2 – condition for commutativ hypergroups and give necessary and sufficient conditions for x ∈ supp π, where π is the Plancherel measure. Finally we apply the general results to characterize supp π in the case of polynomial hypergroups. AMS Subject Classification (1991):43A62, 42C05, 43A07
متن کاملGaussian fluctuations of Young diagrams under the Plancherel measure
We obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the ‘spectrum’ of partitions lwn2N (under the Plancherel measure), thus settling a long-standing problem posed by Logan & Shepp. Namely, under normalization growing like ffiffiffiffiffiffiffiffiffiffi log n p , the corresponding random process in the bulk is shown to converge, in the s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2014
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2014.v10.n4.a1