CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Cristian Lenart, University at Albany

Time:          Wednesday, November 14, at 4:30pm, 

Place:         Bailey Hall 106, Union College

Title:         Multiplication formulas in the K-theory of 
               flag varieties 


Abstract: 

The main object of my talk is an explicit formula for expanding in the
basis of Grothendieck polynomials the product of two such polynomials,
one of which is indexed by an arbitrary permutation, and the other by a
simple transposition; this is a K-theory version of Monk's formula for
Schubert polynomials. Grothendieck and Schubert polynomials are
representatives for Schubert classes in the K-theory and cohomology of
complex flag varieties, respectively. The mentioned formula is in terms
of increasing chains in a certain suborder of the Bruhat order on the
symmetric group with certain labels on its covers. An intermediate
result concerns the multiplication of a Grothendieck polynomial by a
single variable. Some corollaries and a Hopf algebra perspective on
these results will also be presented, if time permits.