Infinitesimal Generators on the Quantum Group SUq(2)

1998 ◽  
Vol 01 (04) ◽  
pp. 573-598 ◽  
Author(s):  
Michael Schürmann ◽  
Michael Skeide
Keyword(s):  
Irreducible Representation ◽  
Quantum Group ◽  
Lie Group ◽  
Lévy Processes ◽  
Levy Processes ◽  
Infinite Dimensional ◽  
Infinitesimal Generators ◽  
Dimensional Irreducible Representation

Quantum Lévy processes on a quantum group are, like classical Lévy processes with values in a Lie group, classified by their infinitesimal generators. We derive a formula for the infinitesimal generators on the quantum group SU q(2) and decompose them in terms of an infinite-dimensional irreducible representation and of characters. Thus we obtain a quantum Lévy–Khintchine formula.

scholarly journals Ergodic multiplier properties

2014 ◽  
Vol 36 (3) ◽  
pp. 794-815 ◽  
Author(s):  
ADI GLÜCKSAM
Keyword(s):  
Irreducible Representation ◽  
Heisenberg Group ◽  
Weak Mixing ◽  
Locally Compact ◽  
Polish Groups ◽  
Infinite Dimensional ◽  
Dimensional Irreducible Representation ◽  
Weakly Mixing

In this article we will extend ‘the weak mixing theorem’ for certain locally compact Polish groups (Moore groups and minimally weakly mixing groups). In addition, we will show that the Gaussian action associated with the infinite-dimensional irreducible representation of the continuous Heisenberg group,$H_{3}(\mathbb{R})$, is weakly mixing but not mildly mixing.

scholarly journals Potential theory of infinite dimensional Lévy processes

2011 ◽  
Vol 261 (10) ◽  
pp. 2845-2876 ◽  
Author(s):  
Lucian Beznea ◽  
Aurel Cornea ◽  
Michael Röckner
Keyword(s):  
Potential Theory ◽  
Lévy Processes ◽  
Levy Processes ◽  
Infinite Dimensional

scholarly journals Lévy Processes in a Step 3 Nilpotent Lie Group

2013 ◽  
Vol 41 (2) ◽  
pp. 367-382
Author(s):  
Maria Gordina ◽  
John Haga
Keyword(s):  
Lie Group ◽  
Lévy Processes ◽  
Levy Processes ◽  
Nilpotent Lie Group

scholarly journals Tangle functors from semicyclic representations

2017 ◽  
Vol 26 (11) ◽  
pp. 1750065
Author(s):  
Nathan Druivenga ◽  
Charles Frohman ◽  
Sanjay Kumar
Keyword(s):  
Irreducible Representation ◽  
Quantum Group ◽  
Lie Algebra ◽  
Representation Formula ◽  
Root Of Unity ◽  
Dimensional Irreducible Representation ◽  
Large Center

Let [Formula: see text] be a [Formula: see text]th root of unity where [Formula: see text] is odd. Let [Formula: see text] denote the quantum group with large center corresponding to the Lie algebra [Formula: see text] with generators [Formula: see text], and [Formula: see text]. A semicyclic representation of [Formula: see text] is an [Formula: see text]-dimensional irreducible representation [Formula: see text], so that [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. We construct a tangle functor for framed homogeneous tangles colored with semicyclic representations, and prove that for [Formula: see text]-tangles coming from knots, the invariant defined by the tangle functor coincides with Kashaev’s invariant.

Irreducible representations of finitely generated nilpotent groups

1977 ◽  
Vol 81 (2) ◽  
pp. 201-208 ◽  
Author(s):  
Daniel Segal
Keyword(s):  
Irreducible Representation ◽  
Nilpotent Group ◽  
Nilpotent Groups ◽  
Irreducible Representations ◽  
Closed Field ◽  
Finitely Generated ◽  
Dimensional Representation ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dimensional Irreducible Representation

1. Introduction. It is well known that every finite-dimensional irreducible representation of a nilpotent group over an algebraically closed field is monomial, that is induced from a 1-dimensional representation of some subgroup. However, even a finitely generated nilpotent group in general has infinite-dimensional irreducible representations, and as a first step towards an understanding of these one wants to discover whether they too are necessarily monomial. The main point of this note is to show how far they can fail to be so.

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