The papers listed below appear in (roughly) reverse chronological
order. All of the files are PostScript.
For most of the papers,
I would be glad to email the pdf file of the
final published version.
A survey of old and new results on this classical subject.
An exposition of some recent developments related to the object in the title.
We introduce and study certain quadratic Hopf algebras related to Schubert
calculus of the flag manifold.
We study a family of operators acting in the span of a Weyl group which
provide a solution of the Yang-Baxter equations of corresponding type.
We study intersections of opposite Bruhat cells in a semisimple complex
Lie group, and associated totally nonnegative varieties.
Cf. P. Littelmann's
Séminaire
Bourbaki talk
We suggest a new combinatorial construction for the cohomology ring
(ordinary or quantum) of the flag manifold.
We express the generating function for the values of an arbitrary virtual
character of the symmetric group (or the Hecke algebra) in terms of its
Frobenius image.
We compute the Gromov-Witten invariants of the flag manifold and derive
the quantum Monk's formula.
We develop efficient algorithms for computing expansions of symmetric
polynomials into Schur functions.
We prove an identity generalizing enumerative formulas of Stanley and
Macdonald related to reduced words for the element of maximal length in
the symmetric group.
We provide: (i) explicit formulas for Lusztig's transition maps related
to the canonical basis of the quantum group of type A; (ii) formulas for
the factorizations of a square matrix into elementary Jacobi matrices;
(iii) a family of new total positivity criteria.
We develop a theory of Schur functions in noncommuting variables.
We introduce and study balanced labellings of diagrams representing
the inversions in a permutation.
Three flavors of Schubert polynomials of types B and C are constructed
and studied.
A new development of the theory of Grothendieck polynomials based on
an exponential solution of the Yang-Baxter equation in the degenerate Hecke
algebra is given.