Résumé : Given a set S of algebras, a natural problem is to discover which algebras from S are (not) isomorphic. A classical way to attack such `distinguishing problems' is by means of invariants. In this talk we will associate to any finite-dimensional algebra A two invariants originating from the asymptotics of the sequence of codimensions c_n(A). This sequence structures algebraic information contained in the ideal of polynomial identities satisfied by A. It was proven by Berele and Regev that the sequence c_n(A) grows asymptotically as c n^t d^n for some constants c, t, and d depending on A. Surprisingly the invariant t is an half-integer and the invariant d even an integer.
In the first half of the talk, we will give an introduction to these concepts and the role of S_n-representation theory hereby. The second part will be based on joint work with Aljadeff and Karasik. Concretely, we will explain the representation and ring theoretical information contained in the numbers t and d. Hereby, the aim will especially be to recall and explain the role of Kemer's theory (developed for his deep solution to the Specht problem) in our work and comment on further use of it.