7,510 research outputs found
On projective representations for compact quantum groups
We study actions of compact quantum groups on type I factors, which may be
interpreted as projective representations of compact quantum groups. We
generalize to this setting some of Woronowicz' results concerning Peter-Weyl
theory for compact quantum groups. The main new phenomenon is that for general
compact quantum groups (more precisely, those which are not of Kac type), not
all irreducible projective representations have to be finite-dimensional. As
applications, we consider the theory of projective representations for the
compact quantum groups associated to group von Neumann algebras of discrete
groups, and consider a certain non-trivial projective representation for
quantum SU(2).Comment: 43 page
A q-Hankel transform associated to the quantum linking groupoid for the quantum SU(2) and E(2) groups
A q-analogue of Erdelyi's formula for the Hankel transform of the product of
Laguerre polynomials is derived using the quantum linking groupoid between the
quantum SU(2) and E(2) groups. The kernel of the q-Hankel transform is given by
the 1\varphi1-q-Bessel function, and then the transform of a product of two
Wall polynomials times a q-exponential is calculated as a product of two Wall
polynomials times a q-exponential.Comment: 11 pages; version 2 includes comments by referee
Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras
Let be a semi-simple Lie algebra with fixed root system, and
the quantization of its universal enveloping algebra. Let
be a subset of the simple roots of . We show that
the defining relations for can be slightly modified in such
a way that the resulting algebra allows a
homomorphism onto (an extension of) the algebra
of functions on the
quantum flag manifold corresponding
to . Moreover, this homomorphism is equivariant with respect to a
natural adjoint action of on
and the standard action of
on .Comment: 19 page
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