October 1, 2013
Mathematics Colloquium lecture today
As part of the math department Colloquium lecture series, Naihuan Jing, North Carolina State University, will present "Vertex Operators and Weyl Characters of Classical Lie Algebras" at 2:30 p.m. today in 122 Cardwell Hall.
The lecture will discuss how Weyl gave an effective algorithm to compute the characters of irreducible modules of classical Lie algebras using tensor powers of the fundamental representations. Weyl's theory can be formulated in the Schur symmetric functions and their orthogonal/symplectic analogs. In this colloquium talk, Jing will talk about the vertex operator approach to classical symmetric functions such as Schur functions, and discuss recent work on vertex operator approach to Weyl's character formulas. This approach can help us obtain several new determinant formulas for Weyl characters as well as giving a new proof and interpretation of the Littlewood duality between the characters of the orthogonal and symplectic groups.
Support for the lecture is provided by National Science Foundation Graduate Research conference grant DMS-1315268.