This award supports work on three main problems: (1) Resolutions of Weyl modules; (2) Intertwining numbers; and (3) Canonical resolutions of determinantal varieties. All of the above problems involve the use of the characteristic-free representation theory of Gl(n) investigated by the principal investigator over the past years. The third problem involves methods of commutative algebra and algebraic geometry as well. Many different algebraic objects can be represented as algebraic sets of transformations of other algebraic objects. Through these representations their structure can be determined. This project is concerned with the representation theory of nxn matrices. This study has applications throughout mathematics and mathematical physics.
