CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Cristian Lenart, University at Albany 

Time:          Wednesday, April 18, at 4:30pm, 

Place:         ES 152A, University at Albany, 

Title:         Combinatorial constructions of Schubert polynomials 


Abstract: 

In this talk I investigate the connections not yet
understood between the existing combinatorial
structures for the construction of Schubert polynomials.
These structures are: certain strand
diagrams called rc-graphs, increasing labeled chains in
the Bruhat order on the symmetric group,
balanced labelings of the diagram of a permutation,
Kohnert diagrams (which are certain diagrams
obtained from the diagram of a permutation by specified
moves), and semistandard Young
tableaux. Recent research on Schubert polynomials has
shown the importance of rc-graphs. Thus,
we relate the other structures to rc-graphs by
constructing new bijections and by studying the
properties of existing bijections. For instance, S.
Billey, W. Jockusch, and R. Stanley, in their work which initiated the
study of rc-graphs, constructed a map from rc-graphs to a
multiset of semistandard Young tableaux. It is
known that the latter are endowed with a crystal graph
structure, given by the action of certain
operators on tableaux, which are relevant to the
representation theory of GL_n(C). We discuss
the way in which these operators can be lifted to
rc-graphs, as well as some consequences.


Refreshments at 4:15 in ES 152.