All Questions
6
questions
0
votes
1
answer
29
views
Summation indices suspiciously don’t align
In Diaconis’ book Group representations in Probability and Statistics, freely online there is the following formula on p. 40 labeled (D-2):
Let $\tau$ be any transposition in $S_n$, $\lambda$ any ...
- 1,092
0
votes
0
answers
53
views
Show $S^\lambda \otimes sgn$ is a simple representation of $S^n$.
Let $\lambda \vdash n$. Identify $S^\lambda \otimes sgn$ as a simple representation of $S^n$.
I know that that $S^\lambda$ is the Specht module (over $\mathbb{C}$) with a set of polytabloids as a ...
- 591
5
votes
1
answer
577
views
Why do partitions correspond to irreps in $S_n$?
As stated for example in these notes (Link to pdf), top of page 8, irreps of the symmetric group $S_n$ correspond to partitions of $n$. This is justified with the following statement:
Irreps of $S_n$ ...
- 7,095
0
votes
1
answer
117
views
Interpreting the table of classification of the partitions of $n$
I am going through A NON-RECURSIVE EXPRESSION FOR THE NUMBER OF IRREDUCIBLE REPRESENTATIONS OF THE SYMMETRIC GROUP $S_n$ by AMUNATEGUI. In table I, the classification of the partitions of n according ...
- 559
0
votes
1
answer
58
views
Young tableaux of partition $3+1+1$ for the conjugacy classes of $S_5$
I just computed the Young tableaux of partition $3+1+1$ for the conjugacy classes of $S_5$. It would be nice if anyone could confirm it's correctness. Thanks.
- 559
3
votes
1
answer
111
views
Symmetry of Plancherel measure (for $S_n$)
For each $n \geq 1$ consider the reverse lexicographical order on the set $P(n)$ of partitions of $n$. Example for $n=7$:
$$
\begin{pmatrix}
\hline
1 & 2 & 3 & 4 & 5 & 6 & 7 ...
- 2,052