On *-representations of $U_{q}(sl(2))$: more real forms

Eduard Vaysleb

Displaying similar documents to “On *-representations of $U_{q} (s l (2))$ : more real forms”

Semilinear relations and *-representations of deformations of so(3)

Yuriĭ Samoĭlenko, Lyudmila Turowska (1997)

Banach Center Publications

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We study a family of commuting selfadjoint operators $= {(A_{k})}_{k = 1}^{n}$ , which satisfy, together with the operators of the family $= {(B_{j})}_{j = 1}^{n}$ , semilinear relations $⅀_{i} f_{i j} () B_{j} g_{i j} () = h ()$ , ( $f_{i j}$ , $g_{i j}$ , $h_{j} : ℝ^{n} \to ℂ$ are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra $U_{q}^{'} (s o (3))$ .

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...

A $q$ -analogue of the centralizer construction and skew representations of the quantum affine algebra.

Hopkins, Mark J., Molev, Alexander I. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Irreducible representations of free products of infinite groups

Wojciech Młotkowski (1996)

Colloquium Mathematicae

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Left-covariant differential calculi on $S L_{q} (N)$

Konrad Schmüdgen, Axel Schüler (1997)

Banach Center Publications

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We study $N^{2} - 1$ dimensional left-covariant differential calculi on the quantum group $S L_{q} (N)$ . In this way we obtain four classes of differential calculi which are algebraically much simpler as the bicovariant calculi. The algebra generated by the left-invariant vector fields has only quadratic-linear relations and posesses a Poincaré-Birkhoff-Witt basis. We use the concept of universal (higher order) differential calculus associated with a given left-covariant first order differential calculus....

Weak c*-Hopf algebras: the coassociative symmetry of non-integral dimensions

Gabriella Böhm, Kornél Szlachányi (1997)

Banach Center Publications

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By allowing the coproduct to be non-unital and weakening the counit and antipode axioms of a C*-Hopf algebra too, we obtain a selfdual set of axioms describing a coassociative quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. It is the same structure that can be obtained by replacing the multiplicative unitary of Baaj and Skandalis with a partial isometry. The algebraic properties, the existence...

Quantum Racah coefficients and subrepresentation semirings.

Sage, Daniel S. (2005)

Journal of Lie Theory

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$T$ -systems and $Y$ -systems for quantum affinizations of quantum Kac-Moody algebras.

Kuniba, Atsuo, Nakanishi, Tomoki, Suzuki, Junji (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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$q$ -analog of Gelfand-Graev basis for the noncompact quantum algebra $U_{q} (u (n, 1))$ .

Asherova, Raisa M., Burdík, Čestmír, Havlíček, Miloslav, Smirnov, Yuri F., Tolstoy, Valeriy N. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Macdonald representations of complex reflection groups.

Morris, Alun O., Mwamba, Patrick (2004)

Séminaire Lotharingien de Combinatoire [electronic only]

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Displaying similar documents to “On *-representations of U q ( s l ( 2 ) ) : more real forms”

Displaying similar documents to “On *-representations of $U_{q} (s l (2))$ : more real forms”