CesareGArdito: /* Covering blocks and covered blocks */

2019-11-28T13:19:37Z

‎Covering blocks and covered blocks

CesareGArdito at 13:19, 28 November 2019

2019-11-28T13:19:16Z

CesareGArdito: Created page with "{{blockbox |title = M(16,14,9) - $B_0(k(A_5 \times A_5))$ |image = |representative = $B_0(k(A_5 \times A_5))$ |defect = (C2)%5E4| $(C_2)^..."$

2019-11-28T13:19:04Z

Created page with "{{blockbox |title = M(16,14,9) - <math>B_0(k(A_5 \times A_5))</math> |image = |representative = <math>B_0(k(A_5 \times A_5))</math> |defect = (C2)%5E4|<math>(C_2)^..."

New page

{{blockbox
|title = M(16,14,9) - <math>B_0(k(A_5 \times A_5))</math>
|image =  
|representative = <math>B_0(k(A_5 \times A_5))</math>
|defect = [[(C2)%5E4|<math>(C_2)^4</math>]]
|inertialquotients = <math>C_3 \times C_3</math>
|k(B) = 16
|l(B) = 9
|k-morita-frob = 1
|Pic-k=  
|cartan = <math>\left( \begin{array}{ccccccccc}
16 & 8 & 8 & 8 & 8 & 4 & 4 & 4 & 4 \\
8 & 8 & 4 & 4 & 4 & 4 & 2 & 2 & 4 \\
8 & 4 & 8 & 4 & 4 & 2 & 4 & 4 & 2 \\
8 & 4 & 4 & 8 & 4 & 4 & 2 & 4 & 2 \\
8 & 4 & 4 & 4 & 8 & 2 & 4 & 2 & 4 \\
4 & 4 & 2 & 4 & 2 & 4 & 1 & 2 & 2 \\
4 & 2 & 4 & 2 & 4 & 1 & 4 & 2 & 2 \\
4 & 2 & 4 & 4 & 2 & 2 & 2 & 4 & 1 \\
4 & 4 & 2 & 2 & 4 & 2 & 2 & 1 & 4
\end{array} \right)</math>
|defect-morita-inv? = Yes
|inertial-morita-inv? = Yes
|O-morita? = Yes
|O-morita = <math>B_0(\mathcal{O} (A_5 \times A_5))</math>
|decomp = See below
|O-morita-frob = 1
|Pic-O =
|PIgroup =
|source? = No
|sourcereps =
|k-derived-known? = Yes
|k-derived = [[M(16,14,8)]], [[M(16,14,9)]]
|O-derived-known? = Yes
|coveringblocks =
|coveredblocks =
|pcoveringblocks =
}}

== Basic algebra ==

== Other notatable representatives ==

== Covering blocks and covered blocks ==

Let <math>N \triangleleft G</math> with prime <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.

If <math>b</math> is in M(16,14,9), then <math>B</math> is also in M(16,14,9).

== Projective indecomposable modules ==

== Irreducible characters ==

All irreducible characters have height zero.

== Decomposition matrix ==
<math>\left( \begin{array}{ccccccccc}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\
1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\
1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\
1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\
1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 \\
1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\
1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\
1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1
\end{array}\right)</math>

[[(C2)%5E4|Back to <math>(C_2)^4</math>]]

@@ Line 46: / Line 46: @@
 Let <math>N \triangleleft G</math> with prime <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.
-If <math>b</math> is in M(16,14,9), then <math>B</math> is also in M(16,14,9).
+If <math>b</math> is in M(16,14,10), then <math>B</math> is also in M(16,14,10).
 == Projective indecomposable modules ==

@@ Line 1: / Line 1: @@
 {{blockbox
-|title = M(16,14,9) - <math>B_0(k(A_5 \times A_5))</math>
+|title = M(16,14,10) - <math>B_0(k(A_5 \times A_5))</math>
 |image = &nbsp;
 |representative =  <math>B_0(k(A_5 \times A_5))</math>

M(16,14,10) - Revision history

CesareGArdito: /* Covering blocks and covered blocks */

CesareGArdito at 13:19, 28 November 2019

CesareGArdito: Created page with "{{blockbox |title = M(16,14,9) - B_0(k(A_5 \times A_5)) |image = |representative = B_0(k(A_5 \times A_5)) |defect = (C2)%5E4|(C_2)^..."

CesareGArdito: Created page with "{{blockbox |title = M(16,14,9) - $B_0(k(A_5 \times A_5))$ |image = |representative = $B_0(k(A_5 \times A_5))$ |defect = (C2)%5E4| $(C_2)^..."$