Titlebook: Representation of Lie Groups and Special Functions; Volume 3: Classical N. Ja. Vilenkin,A. U. Klimyk Book 1992 Springer Science+Business M

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Semisimple Lie Groups and Related Homogeneous Spaces,al simple Lie groups and of corresponding inhomogeneous groups. In the next chapters we study special functions related to non-degenerate series of representations. These special functions depend on many variables and in some cases it is convenient to consider them as functions of matrix argument or

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Group Representations and Special Functions of a Matrix Argument, it let us note that every matrix Λ ∈ P.(.) is representable in the form Λ = .*, where . ∈ ._(., .). and . is the group of diagonal matrices diag (..,... , ..) with .. > 0. We transfer the operation of group multiplication, defined in ._(., .)., into the set P.(.). Namely, for Λ = ....*, . = .... we

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,Representations in the Gel’fand-Tsetlin Basis and Special Functions,of this representation. The restriction of .. onto the subgroup .(. − 1, ℂ) is reducible. It decomposes into the direct sum of all irreducible representations .. of .(. − 1, ℂ) with highest weights .′ = (..,..., ..) for which the betweenness conditions . are satisfied. Each of these representations

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978-3-031-64599-0The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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0302-9743 France, during April 20-22, 2022. .The 31 papers included in this book were carefully reviewed and selected from 73 submissions. They deal with high quality, novel research in intelligent data analysis. .978-3-031-01332-4978-3-031-01333-1Series ISSN 0302-9743 Series E-ISSN 1611-3349

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