Multiplication formulas in the Ktheory of
complex flag varieties
Cristian Lenart
SUNY Albany
May 10,
Special Time: **3:00pm**
2338
ABSTRACT

The main object of the talk is to present some explicit formulas for
expanding the product of certain Grothendieck polynomials in the basis of
such polynomials. Grothendieck polynomials are representatives for
Schubert classes in the Ktheory of the variety of complete flags in the
complex $n$dimensional space; thus, they generalize Schubert
polynomials, which are representatives for Schubert classes in
cohomology. Our formulas are concerned with the multiplication of an
arbitrary Grothendieck polynomial by one indexed by a simple
transposition, and, more generally, by a cycle of the form
$(i,i+1,...,i+p)$; in other words, we generalize Monk's and Pieri's
formulas for Schubert polynomials. Our formulas are in terms of chains in
a suborder of the Bruhat order on the symmetric group (known as kBruhat
order) with certain labels on its covers. We deduce as corollaries A.
Lascoux's transition formula for Grothendieck polynomials, and give a new
formula for the product of a dominant line bundle and a Schubert class in
Ktheory; a previous formula of this type was given by W. Fulton and A.
Lascoux, and later generalized by H. Pittie and A. Ram. Part of this work
is joint with F. Sottile.

Speaker's Contact Info: lenart(atsign)csc.albany.edu
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