This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation… Expand

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic… Expand

Part I. Calculus Of Tableux: 1. Bumping and sliding 2. Words: the plactic monoid 3. Increasing sequences: proofs of the claims 4. The Robinson-Schensted-Knuth Correspondence 5. The… Expand

These are notes from a jointly taught class at the University of Chicago and lectures by the first author in Santa Cruz. Topics covered include: construction of moduli spaces of stable maps,… Expand

Abstract The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan. The natural product of Chow… Expand

The basic tool for a general Riemann-Roch theorem is MacPherson’s graph construction, applied to a complex E. of vector bundles on a scheme Y, exact off a closed subset X. This produces a localized… Expand

We give a formula for the smallest powers of the quantum parameters q that occur in a product of Schubert classes in the (small) quantum cohomology of general flag varieties G/P. We also include a… Expand