Thursday, March 6, 2003
11:30 am, Science Building, Small Auditorium

Steven Jackson

Yale University

Gröbner bases and constructive representation theory

Abstract: Let $R = k[x_1,\dots,x_n]$ be the ring of polynomials in $n$ variables over a field $k$, and let $I$ be an ideal of $R$. The theory of \emph{Gröbner bases} is a system of techniques for algorithmic computation in the quotient ring $R/I$. With the advent of fast computer algebra systems, these techniques have become increasingly important in modern commutative algebra and algebraic geometry. In this talk, I discuss applications of Gröbner basis techniques to a fundamental problem in representation theory: given a linear algebraic group, construct all of its irreducible representations, and give formulas for their matrix elements. No prior knowledge of Gröbner bases is assumed.