Lectures on spin representation theory of symmetric groups

Abstract

The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes, we present a coherent account of the spin counterparts of several classical constructions such as the Frobenius characteristic map, Schur duality, the coinvariant algebra, Kostka polynomials, and Young's seminormal form.

lecture notes for Winter School on Representation Theory, Taipei, December 2010

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• Random strict partitions and random shifted tableaux
• Coinvariant algebras and fake degrees for spin Weyl groups of classical type
• Asymptotic results for Representation Theory
• Cocenters of Hecke-Clifford and spin Hecke algebras
• Linear versus spin: representation theory of the symmetric groups
• A Spin Analogue of Kerov Polynomials
• Supersymmetric monoidal categories
• Frobenius character formula and spin generic degrees for Hecke-Clifford algebra
• A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras
• On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra