Comparing different bases for irreducible symmetric group representations

Abstract: We describe two different bases for irreducible symmetric group representations: the tableaux basis from combinatorics (and from the geometry of a class of varieties called Springer fibers); and the web basis from knot theory (and from the quantum representations of Lie algebras). We then describe new results comparing the bases, e.g. showing that the change-of-basis matrix is upper-triangular, and sketch some applications to geometry and representation theory. This work is joint with H. Russell, as well as with T. Goldwasser and G. Sun.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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