Representations of Virasoro Algebra and an n-Variable Generalization

<strong>Mathematics Seminar of the School of Physical Sciences ---------------------------------------------------------</strong> Title:<strong> Representations of Virasoro Algebra and an n-Variable Generalization</strong> Speaker:<strong> Eswara Rao Senapathi</strong> (Tata Institute of Fundamental Research, Mumbai) Date:<strong> March 14, 2016 </strong> <strong>Abstract:</strong> I will start with definitions of Lie algebra and representations and give some examples. Then we will define Virasoro Algebra and Affine Kac-Moody Lie algerba. We will define modules for Virasoro algebra with bounded multiplicities and also highest weight modules. Then we will state a conjecture, which is now a theorem. We will now define a generalization of Virasoro algebra which is denoted by Der A where A is a Laurent polynomial algebra in n variables. We will define Toroidal Lie algebra which is a generalization of Affine Kac-Moody Lie algebra. We will also define modules for Der A with bounded multiplicities and state a conjecture, which is now a theorem. This will cover the case n=1, which is Virasoro algebra.