The Young-Fibonacci graph YF is an important example (along with the Young lattice) of diierential posets studied by S. Fomin and R. Stanley. For every diierential poset there is a distinguished central measure called the Plancherel measure. We study the Plancherel measure and the associated Markov chain, the Plancherel process, on the Young-Fibonacci graph. We establish a law of large numbers ...

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...

It is proved in [BOO], [J2] and [Ok1] that the joint distribution of suitably scaled rows of a partition with respect to the Plancherel measure of the symmetric group converges to the corresponding distribution of eigenvalues of a Hermitian matrix from the Gaussian Unitary Ensemble. We introduce a new measure on strict partitions, which is analogous to the Plancherel measure, and prove that the...

We obtain the Plancherel decomposition for a reductive symmetric space in the sense of representation theory. Our starting point is the Plancherel formula for spherical Schwartz functions, obtained in part I. The formula for Schwartz functions involves Eisenstein integrals obtained by a residual calculus. In the present paper we identify these integrals as matrix coefficients of the generalized...

In HC], Harish-Chandra derived the Plancherel formula on p-adic groups. However, to have an explicit formula, one will have to compute the measures appearing in the formula. Here, we compute Plancherel measures on Sp 4 over p-adic elds explicitly.

So there 5 partitions for 4. Assign each partition with a probability, we then get a probability measure on them. Different ways of assigning probabilities: Uniform measure Plancherel measure Jack measure Restricted uniform measure Restricted Jack measure. We will study the properties of r.v.’s (k1, k2, . . .), a random partition of n. Example 2. As n→∞, under the Plancherel measure, k1 − 2 √ n...

We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the most continuous part of the Plancherel formula by means of a residue calculus. In the course of the present paper we also obtain new proofs of the uniform t...

Abstract. In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study the Fourier and Fourier-Plancherel transforms and prove the Plancherel theorem for compact groupoids. We also study the central functions in the algebra of squa...

Let Mn stand for the Plancherel measure on Yn, the set of Young diagrams with n boxes. A recent result of R. P. Stanley (arXiv:0807.0383) says that for certain functions G defined on the set Y of all Young diagrams, the average of G with respect to Mn depends on n polynomially. We propose two other proofs of this result together with a generalization to the Jack deformation of the Plancherel me...

For a real or p-adic connected reductive group G, Harish-Chandra introduced the Plancherel measure on the tempered dual Ĝtemp and founded the Plancherel formula [7, 18] relating functions on G to functions on Ĝtemp. While the Plancherel measure is equal to the formal degree for square-integrable representations, there has been no similar interpretation for tempered but nonsquare-integrable repr...