Harmonic analysis on the infinite symmetric group
نویسندگان
چکیده
منابع مشابه
An introduction to harmonic analysis on the infinite symmetric group
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory — harmonic analysis for noncommutative groups with infinite–dimensional dual space. I omitted detailed proofs but tried to explain the main ideas of the theory and its connections with other fields. The fact that irreducible representations of the groups in question depend on i...
متن کاملClosed subgroups of the infinite symmetric group
Let S = Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G1, G2 6 S let us write G1 ≈ G2 if there exists a finite set U ⊆ S such that 〈G1 ∪U 〉 = 〈G2 ∪U 〉. It is shown that the subgroups closed in the function topology on S lie in precisely four equivalence classes under this relation. Which of these classes a closed subgroup G belongs to depends on which ...
متن کاملThe Problem of Harmonic Analysis on the Infinite–dimensional Unitary Group
The goal of harmonic analysis on a (noncommutative) group is to decompose the most “natural” unitary representations of this group (like the regular representation) on irreducible ones. The infinite–dimensional unitary group U(∞) is one of the basic examples of “big” groups whose irreducible representations depend on infinitely many parameters. Our aim is to explain what the harmonic analysis o...
متن کاملHarmonic Analysis on Real Reductive Symmetric Spaces
Let G be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over R. Let σ be an involution of the Lie group G, H an open subgroup of the subgroup of fixed points of σ. One decomposes the elements of L(G/H) with the help of joint eigenfunctions under the algebra of le...
متن کاملDisjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group
In the context of the problem of harmonic analysis on the group U(∞) a family of representations Tz,w was constructed and studied in the papers [Olsh2] and [BO]. These representations depend on two complex parameters and provide a natural generalization of the regular representation for the case of “big” group U(∞). The representation Tz,w does not change if z or w is replaced by z or w, respec...
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: Inventiones mathematicae
سال: 2004
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-004-0381-4