2
votes
1answer
98 views

Rep of Non-Commutative Monoids

Let M be a non-commutative monoid. It is possible that all representation of M are one dimensional ?? (for groups the answer is negative. Take a non zero x=[a,b]. Take a representation where x does ...
5
votes
0answers
330 views

Duality between conjugacy classes and irreducible characters for finite monoids?

Qiaochu's answer to this question suggests that the proper way to view the bijection between conjugacy classes and irreducible complex representations of a finite group is via a duality. My question ...
3
votes
0answers
232 views

Is there a homological way to compute quiver presentations?

I have recently been studying with colleagues the representation theory of certain finite monoids that come up in probability theory and combinatorics, see Ken Brown's beautiful survey here. These ...
4
votes
0answers
211 views

What is the pro-algebraic completion of the free semigroup on one generator?

This question is motivated by an attempt to understand what is going on in Tom's post from a certain point of view. Let $\mathbb N^+$ be the free semigroup on one generator (so the positive natural ...
9
votes
1answer
371 views

Is the following construction of the 0-Hecke monoid (well) known?

Let W be a Coxeter group with Coxeter generators S. The corresponding 0-Hecke monoid H(W) has generating set S, the braid relations of W and the relations that each element of S is an idempotent. If ...
40
votes
11answers
4k views

Why aren't representations of monoids studied so much?

It seems to me like every book on representation theory leaps into groups right away, even though the underlying ideas, such as representations, convolution algebras, etc. don't really make explicit ...
5
votes
1answer
315 views

Representations of products of groups (and monoids)

I have very little knowledge of representation theory, but the following has come up in my summer undergrad research project (relates to conformal field theory and geometric function theory). Suppose ...