Lectures on geometric constructions of the irreducible representations of GL_n

Abstract

We give an exposition of three geometric constructions of the irreducible representations of GL_n. In particular, we discuss Borel-Weil theory, the Ginzburg construction, and the geometric Satake construction. We also explain how to deduce the Ginzburg construction from the geometric Satake equivalence. These are lecture notes for a lecture series at the Summer School on geometric representation theory and extended affine Lie algebras held at University of Ottawa in June 2009.

17 pages

References in corpus (1)

• Relation between two geometrically defined bases in representations of $G{L}_n$

Cited by in corpus (2)

• An introduction to diagrammatic algebra and categorified quantum sl(2)
• Lectures on geometric realizations of crystals