Harmonic analysis on a finite homogeneous space II: The Gelfand–Tsetlin decomposition
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Fabio Scarabotti
Abstract
In this paper, we continue the analysis of [Scarabotti, Tolli, Proc. London Math. Soc.: 2009] on finite homogeneous spaces whose associated permutation representation decomposes with multiplicity. We extend the theory of Gelfand–Tsetlin bases to permutation representations. Then we study several concrete examples on the symmetric groups, generalizing the Gelfand pair of the Johnson scheme. We also extend part of the Okounkov–Vershik theory to the Young permutation module Ma. In particular we constuct explicit Gelfand–Tsetlin bases for the representation Sn–1,1. We also give an explicit Gelfand–Tsetlin decomposition for the permutation module associated with a three-parts partitions, using James reformulation of the Young rule by means of intertwining operators (Radon transforms). Several statistical applications, refining previous work by Diaconis, are given. Finally, the spectrum of several invariant operators is determined.
© de Gruyter 2010
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- Harmonic analysis on a finite homogeneous space II: The Gelfand–Tsetlin decomposition
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- Amplitude inequalities for Differential Graded modules
- Homogeneous Lagrangian submanifolds of positive Euler characteristic
- Kostant convexity for affine buildings
- Algebraic monodromy and obstructions to formality
- Capacity and potentials on curves
- New characterizations of pseudo-coherent rings
- Le module de continuité des valeurs au bord des fonctions propres et des formes automorphes
Articles in the same Issue
- Inhomogeneous Strichartz estimates
- Some characterizations of finite groups in which semipermutability is a transitive relation
- Fine gradings on the Lie algebra
- Harmonic analysis on a finite homogeneous space II: The Gelfand–Tsetlin decomposition
- Regularity results for the gradient of solutions of linear elliptic systems with VMO-coefficients and L1,λ data
- Amplitude inequalities for Differential Graded modules
- Homogeneous Lagrangian submanifolds of positive Euler characteristic
- Kostant convexity for affine buildings
- Algebraic monodromy and obstructions to formality
- Capacity and potentials on curves
- New characterizations of pseudo-coherent rings
- Le module de continuité des valeurs au bord des fonctions propres et des formes automorphes
