# Column stabilizers of a Young tableaux (Rep. theory)

I'm a bit confused about the notion of a column stabilizer for a Young tableaux. I know that if I have the following tableaux $T$:

$[1][2][3]$

$[4][5][6]$

The column stabilizer $C(T)$ will be (based on notes): $\{(1), (14), (25), (36), (14)(25), (14)(36), (25)(36), (14)(25)(26)\}$

But I'm just not sure if I am making some super naïve assumption that I should not be making.

Let's say I have another Young tableaux $T'$:

$[1][3][5]$

$[2][4]$

Would $C(T')$ be $\{(1), (12), (24), (12)(34)\}$? Thank you for your help.

• If you write $(34)$ in place of $(24)$, then yes. – Dustan Levenstein May 7 '17 at 21:01
• Of course, a better test of whether you are correctly understanding definitions would be to consider a Young Tableau with a column of size 3 or more. – Dustan Levenstein May 7 '17 at 21:02
• I meant to write $(24)$, thanks. Also, if $T$ is a Young tableau, what exactly does the notation $\{T\}$ mean? – Nażysław Zbyłutowicz May 7 '17 at 21:06
• @NażysławZbyłutowicz: It depends on the book you're reading, a lot of the notation is nonstandard. I know in Fulton's "Young Tableaux" he takes $\{T\}$ to mean the equivalence class of $T$, modulo rearranging within rows. – Joppy May 8 '17 at 4:19