An invitation to the generalized saturation conjecture

An Invitation to the Generalized Saturation Conjecture

We report about some results, interesting examples, problems and conjectures revolving around the parabolic Kostant partition functions, the parabolic Kostka polynomials and “saturation” properties of several generalizations of the Littlewood–Richardson numbers.

The Saturation Conjecture

The purpose of this exposition 1 is to give a simple and complete treatment of Knutson and Tao's recent proof of the saturation conjecture [8]. If λ is a partition of length at most n, let V λ denote the corresponding highest weight representation of GL n (C). Define This set is important in numerous areas besides representation theory. In Schubert calculus it describes when an intersection of ...

The Saturation Conjecture ( After

The purpose of this exposition 1 is to give a simple and complete treatment of Knutson and Tao's recent proof of the saturation conjecture [8]. If λ is a partition of length at most n, let V λ denote the corresponding highest weight representation of GL n (C). Define This set is important in numerous areas besides representation theory. In Schubert calculus it describes when an intersection of ...

An Invitation to Play

Parity games and their subclasses and variants pop up in various contexts: μ-calculus, tree automata, program verification [3, 1, 8]. Such games provide only binary information indicating the winning player. However, in classical games theory [12] the emphasis is rather on how much we win or lose. Can we incorporate the information about the profits and losses into parity games?

An Invitation to Topology