Title: Projective representations of Heisenberg groups
Speaker: Sumana Hatui (IISc Mathematics)
Date: 13 March 2020
Time: 3 pm
Venue: LH-1, Mathematics Department
The theory of projective representations of groups, extensively
studied by Schur, involves understanding homomorphisms from a
group into the projective linear groups. By definition, every
ordinary representation of a group is also projective but the
converse need not be true. Therefore understanding the projective
representations of a group is a deeper problem and many a times
also more difficult in nature. To deal with this, an important
role is played by a group called the Schur multiplier.
In this talk, we shall describe the Schur mutiplier of the discrete
as well as the finite Heisenberg groups and their $t$-variants.
We shall discuss the representation groups of these Heisenberg
groups and through these give a construction of their finite
dimensional complex projective irreducible representations.