#### Room 326

#### An Introduction to Schubert Polynomials

#### Vijay Ravikumar

##### Chennai Mathematical Institute

*We will go over Lascoux and Schutzenberger's construction of the "Schubert polynomials". In particular, we will review the Hasse diagram corresponding to the symmetric group S_n, and then introduce the divided difference operators, which allow us to "push" certain polynomials down the Hasse diagram. Starting with a "nice" polynomial at the very top of the diagram, we will construct the set of Schubert polynomials, one for each element of S_n. We shall see how these polynomials generalize Schur polynomials, and how they convey important geometric information about the manifold of compete flags on the vector space C^n. Note that Prof. Takeshi Ikeda will talk about certain generalizations of Schubert polynomials in a later seminar.*

Done