Completely Splittable Representations of Symmetric Groups

Completely Splittable Representations of Symmetric Groups

The Ext-quiver for completely splittable representations of the symmetric group

Kleshchev has recently [7] classi®ed those modules for the symmetric group which have semisimple restriction to any Young subgroup. We determine Ext K Sd …D ;D m† where D l and D m are K Sd -modules of this type, called completely splittable. As a corollary of this and recent work of Kleshchev and Nakano, we can determine ExtGL n…K†……L…l†;L…m†† for certain simple GLn…K†-modules L…l† and L…m†. 1...

Representations of symmetric groups

In this thesis we study the ordinary and the modular representation theory of the symmetric group. In particular we focus our work on different important open questions in the area. 1. Foulkes’ Conjecture In Chapter 2 we focus our attention on the long standing open problem known as Foulkes’ Conjecture. We use methods from character theory of symmetric groups to determine new information on the...

Representations of Symmetric Groups

A surprising theorem in the modular representation theory of symmetric groups uses induction and restriction functors to define an action of an affine Kac-Moody special linear algebra on the level of Grothendieck groups. This action identifies the direct sum of Grothendieck groups with an integrable highest weight module of the Kac-Moody algebra. The purpose of this write-up is to provide a gen...

Symmetric Representations of Knot Groups

In this paper we give an explicit and constructive description of the pairs (p. A) of elements in the symmetric group S, which can be realized as the image of the meridian-longitude pair of some knot K in the 3-sphere S3 under a representation xi (S’ K) -t S,,. The result is applied to give an otherwise nonobvious restriction on the numbers of branch curves of a branched covering , of S’, answe...