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Results tagged with symmetric-groups
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user 4366
The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.
3
votes
What is known about the centraliser of the Hecke algebra in the affine Hecke algebra?
This is not a complete answer, but does give some information.
In addition to having an embedding of the Iwahori-Hecke algebra into the affine Hecke algebra, $\iota:H_n^{\mathrm{fin}}\hookrightarrow …
- 1,472
1
vote
Accepted
Homomorphisms from irreducible spaces to reducible spaces
I assume you are talking about representations of $S_n$ over $\mathbb{C}$. In this case, $\mathbb{C}S_n$ is left semi-simple by Maschke's Theorem, so every representation of $S_n$ is a direct sum of i …
- 1,472