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2 votes
1 answer
61 views

Invariant theory for unitary groups $\mathcal{U}(n)$

I'm trying to understand the invariant theory of the unitary groups $\mathcal{U}(n)$ on tensor powers of their standard representations $V^{\otimes p} \otimes (V^*)^{\otimes q}$. Let $\mathcal{U}(n)$ ...
Greg Zitelli's user avatar
  • 1,104
6 votes
0 answers
148 views

What about Hopf algebra and fusion structures for intertwiner algebras?

Let $G$ be a complex, reductive group and let $V_1, \dotsc, V_r$ be a collection of finite dimensional, irreducible complex representations of $G$. Let $\mathcal{A} = \mathrm{End}_G(V_1 \otimes \dotsb ...
Jeanne Scott's user avatar
  • 2,137
2 votes
0 answers
132 views

Complete list of indecomposable representations of Temperley-Lieb algebras at roots of unity?

The Temperley Lieb algebra $TL_n$ at roots of unity is not semisimple. The standard representations $V_{n,p}$ are indecomposable but, in general, not irreducible. If $K_{n,p}$ is the sub-...
Maithreya Sitaraman's user avatar
41 votes
3 answers
3k views

Why is there such a close resemblance between the unitary representation theory of the Virasoro algebra and that of the Temperley-Lieb algebra?

For those who aren't familiar with the Virasoro or Temperley-Lieb algebras, I include some definitions: • The (universal envelopping algebra of the) Virasoro algebra is the $\star$-algebra $...
André Henriques's user avatar
18 votes
7 answers
2k views

ubiquity, importance of path algebras

I work in planar algebras and subfactors, where the idea of path algebras on a graph (alternately known as graph algebras, graph planar algebras, etc.) is quite useful. The particular result I'm ...
Emily Peters's user avatar
  • 1,089