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Results tagged with rt.representation-theory
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user 21857
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
10
votes
1
answer
363
views
A Realization Problem for Character Tables
Given an $n\times n$ table of complex numbers, are there known sufficient conditions for the table to be the character table of a finite group? Representation theory gives plenty of necessary conditi …
- 1,261
7
votes
2
answers
221
views
Irreducibility of Coxeter graphs as a function of generating sets
Given a Coxeter system $(W, S)$, we can form its Coxeter graph, and say that the system is irreducible if the graph is connected. Now, irreducibility is not solely a function of $W$; it depends also o …
- 1,261
9
votes
2
answers
1k
views
Character table entries and sums of roots of unity
It is well-known that the entries of the character table of a finite group are sums of roots of unity.
Question: Is the converse true? Explicitly, given $z\in \mathbb{Z}[\mu_\infty]$, can I find a f …
- 1,261