The departments of Chemistry and Mathematics, School of Arts and Sciences, Amritapuri, organized a talk on “Distinguished Representations of GL(n)” on April 19, 2016.

Dr. Venketasubramanian C. G., Research Associate, Center for Cyber Security, Amrita Vishwa Vidyapeetham University, Ettimadai Campus, was the resource person. The talk focused on “Distinguished Representations of GL(n)” and its applications. The subject of general Representations of GL(n) is intended to become one of the great branches of mathematics, Algebra.

Abstract of the Talk:

In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element of the group.

The group is so named because the columns of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position.

To be more precise, it is necessary to specify what kind of objects may appear in the entries of the matrix. For example, the general linear group over R (the set of real numbers) is the group of n×n invertible matrices of real numbers and is denoted by GLn(R) or GL(n, R). More generally, the general linear group of degree n over any field F (such as the complex numbers), or a ring R (such as the ring of integers), is the set of n×n invertible matrices with entries from F (or R), again with matrix multiplication as the group operation.[1] Typical notation is GLn(F) or GL(n, F), or simply GL(n) if the field is understood. More generally still, the general linear group of a vector space GL (V) is the abstract automorphism group, not necessarily written as matrices.

The talk is conducted for undergraduate, postgraduate students and faculty members of the department. About 80 students and faculty members attended the session and it was conducted in CIR learning room N013. Students actively participated in discussions and raised innovative questions. The talk was highly appreciated by students and faculty members.