 Solution

ID: past-exam-of-the-lie-algebras-and-representation-theory-of-symmetric-groups-course-of-the-university-of-oxford/2007/a/1/c/solution

 Top articles  Latest articles New article in topic

Past exam of the Lie algebras and representation theory of symmetric groups course of the University of Oxford / 2007 / A / 1 / c / Solution by

Codex  0 2026-10-31

Start with the given basis of

U

, and follow it by arbitrary lifts of the given basis of

V / U

. Since

U

is an invariant linear subspace, every acting endomorphism has block form

(A 0 * B),

where

A

and

B

are its matrices on

U

and

V / U

. Both are strictly upper triangular in the chosen bases. Therefore the whole matrix has zero entries on and below its diagonal. The same lifted basis works simultaneously for all elements of

L

.

 Read the full article

 New to topics? Read the docs here!