Displaying similar documents to “Semilinear relations and *-representations of deformations of so(3)”

On *-representations of U q ( s l ( 2 ) ) : more real forms

Eduard Vaysleb (1997)

Banach Center Publications

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The main goal of this paper is to do the representation-theoretic groundwork for two new candidates for locally compact (nondiscrete) quantum groups. These objects are real forms of the quantized universal enveloping algebra U q ( s l ( 2 ) ) and do not have real Lie algebras as classical limits. Surprisingly, their representations are naturally described using only bounded (in one case only two-dimensional) operators. That removes the problem of describing their Hopf structure ’on the Hilbert space...

On representation theory of quantum S L q ( 2 ) groups at roots of unity

Piotr Kondratowicz, Piotr Podleś (1997)

Banach Center Publications

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Irreducible representations of quantum groups S L q ( 2 ) (in Woronowicz’ approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the case of q being an odd root of unity. Here we find the irreducible representations for all roots of unity (also of an even degree), as well as describe “the diagonal part” of the tensor product of any two irreducible representations. An example of a not completely reducible representation is given. Non-existence of Haar functional is proved. The corresponding...

Representations and Positive Definite Functions on Hypergroups

Nasr-Isfahani, A. (1999)

Serdica Mathematical Journal

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Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.