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- W79084669 abstract "A fundamental problem in representation theory is that of describing the unitary representations of a locally compact group G as a direct integral of simpler representations. The “abstract” problem (i.e., the problem of determining when such decompositions exist) takes up a good part of Mackey’s Chicago lecture notes ↑l6←; it is shown there that if G is Type I, then the problem has a satisfactory solution. The “concrete” problem (given G and a representation ρ, decompose ρ) can be considerably harder. For instance, if G is a semisimple Lie group andΓ is a discrete, cocompact subgroup, then the quasi-regular representation of G on L2(ΓG) is known to be a direct sum of irreducibles, each occurring with finite multiplicity, but little is known about which irreducibles appear. (See ↑l6←.)" @default.
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- W79084669 date "1987-01-01" @default.
- W79084669 modified "2023-09-24" @default.
- W79084669 title "Kirillov Orbits and Direct Integral Decompositions on Certain Quotient Spaces" @default.
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- W79084669 doi "https://doi.org/10.1007/978-1-4612-4722-7_2" @default.
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