IPDF progress seminar
Speaker: Dr. Manabendra Giri, IIT Bombay
Host: Sutanu Roy
Title: Quantum Unitary Groups with Complex Deformation Parameters
Time, day and date: 4:30:00 PM – 5:30:00 PM, Friday, August 28
Venue: Ramanujan Hall
Abstract: In this talk, I want to discuss a family of quantum unitary groups associated with complex deformation parameters. I begin with the construction of the quantum unitary group $U_{q,\Phi}(n)$, extending the construction of Zhang and Zhao for $n=2$ to higher dimensions. I show that $U_{q,\Phi}(n)$ admits the structure of a compact quantum group in the sense of Woronowicz.

I then focus on the case $n=3$ and study the irreducible $*$-representations of the corresponding $C^*$ algebra $C(U_{q,\Phi}(3))$.It is possible to describe these representations in terms of irreducible representations of the rotational $C^*$-algebra generated by three unitaries.

Finally, I consider the crystalized algebra $C(U_{0,\Phi}(3))$ and investigate its $*$-irreducible representations.