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Jun
10
comment A question in combinatorics
Any such sequence.
Jun
10
revised A question in combinatorics
deleted 179 characters in body
Jun
10
asked A question in combinatorics
Jun
9
comment Is there any relation between the Gershgorin circles of a matrix and its resolvent?
I corrected the question!
Jun
9
revised Is there any relation between the Gershgorin circles of a matrix and its resolvent?
added 7 characters in body
Jun
9
asked Is there any relation between the Gershgorin circles of a matrix and its resolvent?
May
30
comment What is the use and motivation for this particular concept in permutations?
In the permutation "54231", if one removes the "2" then one is left with "5431" and this after re-ranking is the permutation "4321" and NOT the permutation "4231". So I am not getting your argument about what you mean if you say that "54231 contains the permutation 4231 at positions 1,3,4,5"
May
30
comment What is the use and motivation for this particular concept in permutations?
Thanks for the explanations! But 54231 contains the pattern 4231 even at positions 4,2,3,1 - right?
May
2
revised How does GAP understand $SL_2(\mathbb{F}_3)$?
added 23 characters in body
May
2
revised How does GAP understand $SL_2(\mathbb{F}_3)$?
added 44 characters in body
May
2
revised How does GAP understand $SL_2(\mathbb{F}_3)$?
added 107 characters in body
May
2
comment How to read GAP's output on “IrreducibleRepresentations”?
Can you kindly give the link to where in the manual this is explained? In the manual I can't even find an index to see what is the meaning of Z(3) !
May
2
asked How does GAP understand $SL_2(\mathbb{F}_3)$?
May
2
comment How to read GAP's output on “IrreducibleRepresentations”?
@Max Its not that clear. When one is asking for " IrreducibleRepresentations(SL(2,3))" it makes sense that the matrices it returns are over the complex field as thats where the representations are. Then GAP uses something called E(3) which I believe is the primitive cuberoot of unity. But when one is asking for List(GeneratorsOfGroup(SL(2,3))); what is this Z(3) that GAP is using? When one is listing out the generators of SL(2,3) the matrices should be 2x2 matrices with entries in F_3.
May
1
comment How to read GAP's output on “IrreducibleRepresentations”?
Do you understand what I am trying to say? Its not clear as to in which representation of F_3 is it possible for 0, 1 and a primitive root of unity to occur together! Why is GAP shifting from the Z(3) that it uses in the generators to the E(3) that it uses later?
May
1
comment How to read GAP's output on “IrreducibleRepresentations”?
This interpretation of E(3) or Z(3) doesn't make sense. Firstly is E(3) the same as Z(3) ? I think there are two natural ways to think of F_p, - as the set {0,1,2,3..,p-1} - or as the set {0,1,x,x^2,...,x^{p-2}} where x is the (p-1)^th primitive root of unity Now what is GAP thinking when it says that [[0,1],[Z(3),0]] is one its generators of SL_2(F_3)? F_3 can either be represented in {0,1,-1} or as {0,1,2} What is Z(3) or E(3) ?
May
1
comment How to read GAP's output on “IrreducibleRepresentations”?
This is not clear. What is this E(3) ? If 0 is occurring in the generators that GAP is using then it is having F_3 in the additive representation which has elements (0,1,-1) and there is no clear meaning to E(3). What is permutation representation that GAP is using to write its generators in a cycle decomposed notation?
Apr
30
comment What is the permutation representation of $SL_2(\mathbb{F}_p)$, $PSL_2(\mathbb{F}_p)$ and $GL_2(\mathbb{F}_p)$?
For q a prime power, isn't the permutation action of GL_2(F_q) or SL_2(F_q) on F_q^2 giving a q^2 dimensional representation? I would like to break this into irreps over C - obviously.
Apr
30
comment What is the permutation representation of $SL_2(\mathbb{F}_p)$, $PSL_2(\mathbb{F}_p)$ and $GL_2(\mathbb{F}_p)$?
What is C(X)? Given the permutation action of G on X which is the |X| sized representation here?
Apr
30
comment What is the permutation representation of $SL_2(\mathbb{F}_p)$, $PSL_2(\mathbb{F}_p)$ and $GL_2(\mathbb{F}_p)$?
(1) Both GL_2(F_q) and SL_2(F_q) have a (q+1)-dimensional representation on P(F_q^2) - agreed? (2) There is no irrep of GL_2(F_q) or SL_2(F_q) which is of dimension q^2 (as this permutation representation is) then how can this be irreducible? (you can see the irrep sizes here, groupprops.subwiki.org/wiki/…, groupprops.subwiki.org/wiki/…