A bstract We compute the exact, all energy scale, 4-point function of the large N
doublescaled SYK model, by using only combinatorial tools and relating the correlation …

This book provides an introduction to the theory of quantum groups with emphasis on their
duality and on the setting of operator algebras. Part I of the text presents the basic theory of …

We develop a general framework to deal with the unitary representations of quantum groups
using the language of C*-algebras. Using this framework, we prove that the duality holds in …

These lecture notes are intended as an introduction to the theory of locally compact quantum
groups that are studied in the framework of operator algebras, ie C*-algebras and von …

A certain class of unitary representations of has the property of being simultanenously a
representation of for a particular choice of˜ q (q). Faddeev has proposed to unify the …

We give complete detail of the description of the GNS representation of the quantum plane A
and its dual A as a von Neumann algebra. In particular, we obtain a rather surprising result …

We introduce the notion of identity component of a compact quantum group and that of total
disconnectedness. As a drawback of the generalized Burnside problem, we note that totally …

In the first part of the paper kernels are constructed which meromorphically extend the
Macdonald-Koornwinder polynomials in their degrees. In the second part the kernels …

We define for real $ q $ a unital $* $-algebra $ U_q (\mathfrak {sl}(2,\mathbb {R})) $
quantizing the universal enveloping $* $-algebra of $\mathfrak {sl}(2,\mathbb {R}) $. The …

The main goal is to interpret the Askey-Wilson function and the corresponding transform pair
on the quantum SU (1, 1) group. A weight on the C*-algebra of continuous functions …